8th Grade. 3-Dimensional Solids. Slide 1 / 97 Slide 2 / 97. Slide 3 / 97. Slide 3 (Answer) / 97. Slide 4 / 97. Slide 5 / 97.
|
|
- Bruce Floyd
- 5 years ago
- Views:
Transcription
1 Slide / 97 Slide 2 / 97 8th Grade D Geometry Slide / 97 Table of ontents Slide () / 97 Table of ontents -Dimensional Solids Volume Prisms and ylinders Pyramids, ones & Spheres More Practice/ Review Glossary & Standards lick on the topic to go to that section -Dimensional Solids Volume lick on the topic to go to that section Prisms and ylinders Vocabulary Words are bolded Pyramids, in ones the presentation. & Spheres The text box the word is in is then More Practice/ linked Review to the page at the end of the presentation with the Glossary & Standards word defined on it. Teacher Notes Slide 4 / 97 Slide 5 / 97 -Dimensional Solids The following link will take you to a site with interactive -D figures and nets. Return to Table of ontents
2 Slide 6 / 97 Polyhedron Polyhedron A -D figure whose faces are all polygons. Sort the figures into the appropriate side. Slide 7 / 97 -Dimensional Solids ategories & haracteristics of -D Solids: Prisms. Have 2 congruent, polygon bases which are parallel to one another click to reveal 2. Sides are rectangular (parallelograms). Named by the shape of their base Polyhedron Not Polyhedron Pyramids. Have polygon base with a vertex opposite it 2. Sides are triangular click to reveal. Named by the shape of their base Slide 8 / 97 Slide 9 / 97 -Dimensional Solids ategories & haracteristics of -D Solids: -Dimensional Solids Vocabulary Words for -D Solids: ylinders. Have 2 congruent, circular bases which are parallel to one click another to reveal 2. Sides are curved Polyhedron Face A -D figure whose faces are all polygons (Prisms & Pyramids) Flat surface of a Polyhedron ones. Have circular bases with a vertex opposite it 2. Sides are curved click to reveal Edge Line segment formed where 2 faces meet Vertex (Vertices) Point where or more faces/edges meet Slide 0 / 97 Sort the figures. If you are incorrect, the figure will be sent back. Name the figure. Slide / 97 A D E F Rectangular Prism Triangular Pyramid Hexagonal Prism Rectangular Pyramid ylinder one
3 Slide () / 97 Slide 2 / 97 Name the figure. 2 Name the figure. A Rectangular Prism A Rectangular Pyramid D E F Triangular Pyramid Hexagonal Prism Rectangular Pyramid ylinder one D D E F Triangular Prism Octagonal Prism ircular Pyramid ylinder one Slide 2 () / 97 Slide / 97 2 Name the figure. Name the figure. A Rectangular Pyramid A Rectangular Pyramid D Triangular Prism Octagonal Prism ircular Pyramid E D Triangular Pyramid Triangular Prism Hexagonal Pyramid E ylinder E ylinder F one F one Slide () / 97 Slide 4 / 97 Name the figure. 4 Name the figure. A D E F Rectangular Pyramid Triangular Pyramid Triangular Prism Hexagonal Pyramid ylinder one A D E F Rectangular Prism Triangular Prism Square Prism Rectangular Pyramid ylinder one
4 Slide 4 () / 97 Slide 5 / 97 4 Name the figure. 5 Name the figure. A D E F Rectangular Prism Triangular Prism Square Prism Rectangular Pyramid ylinder one A A D E F Rectangular Prism Triangular Pyramid ircular Prism ircular Pyramid ylinder one Slide 5 () / 97 Slide 6 / 97 5 Name the figure. A Rectangular Prism Triangular Pyramid ircular Prism D ircular Pyramid E ylinder F one F For each figure, find the number of faces, vertices and edges. an you figure out a relationship between the number of faces, vertices and edges of -Dimensional Figures? Name Faces Vertices Edges ube Rectangular Prism Triangular Prism Triangular Pyramid Square Pyramid Pentagonal Pyramid Octagonal Prism Math Practice Slide 7 / 97 Euler's Formula Slide 8 / 97 6 How many faces does a pentagonal prism have? F + E + 2 Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices.
5 Slide 8 () / 97 6 How many faces does a pentagonal prism have? Slide 9 / 97 7 How many edges does a rectangular pyramid have? 7 Slide 9 () / 97 7 How many edges does a rectangular pyramid have? Slide 20 / 97 8 How many vertices does a triangular prism have? 8 Slide 20 () / 97 8 How many vertices does a triangular prism have? Slide 2 / 97 9 How many faces does a hexagonal pyramid have? 6
6 Slide 2 () / 97 9 How many faces does a hexagonal pyramid have? Slide 22 / 97 0 How many vertices does a triangular pyramid have? 7 Slide 22 () / 97 Slide 2 / 97 0 How many vertices does a triangular pyramid have? 4 Volume Return to Table of ontents Volume Label - Units click to or reveal cubic units Slide 24 / 97 Volume - The amount of space occupied by a -D Figure click to reveal - The number of cubic units needed to FILL a -D Figure (layering) Volume Label - Units click to or reveal cubic units Slide 24 () / 97 Volume MP.6: Attend to Precision. - The amount of space occupied by a -D Figure click to reveal - The number of cubic units needed to FILL a -D Figure (layering) Ask: What labels (or units) should we use with our answers? Math Practice
7 Slide 25 / 97 Volume Activity Slide 25 () / 97 Volume Activity lick the link below for the activity. Lab #: Volume Activity lick the link below for the activity. The URL for the lab is: Teacher Notes Lab #: Volume math/8th-grade-math/dgeometry/volume-activity/ Activity Slide 26 / 97 Slide 27 / 97 Volume Volume of Prisms & ylinders: Volume of Prisms & ylinders Area of click ase to reveal x Height, or h Return to Table of ontents Area Formulas: Rectangle = lw or bh Triangle = bh or 2 ircle = πr 2 click to reveal click to reveal click to reveal 2 (bh) Slide 28 / 97 Slide 28 () / 97 Find the Volume Find the Volume 2 m 5 m 8 m 2 m 5 m VOLUME: VOLUME: 2 h 8 m x 5 l w h 0 (Area of ase) x 8 (Height) m 80 m
8 Slide 29 / 97 Find the Volume Use.4 as your value of π. Slide 29 () / 97 Find the Volume Use.4 as your value of π. 9 yd 0 yd 9 yd VOLUME: 9 x 9 80 yd x x 0 (Height) yd (Area of ase) VOLUME: h r 2 h yd Slide 0 / 97 Slide 0 () / 97 A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used.4 as her value of π. Is she correct? Explain your reasoning. Start by calculating the volume of both cylinders. (.4)(2) 2 (5) (.4)(4)2 (5) 62.8 cm 25.2 cm click the question. click No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples. click Find the Volume A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder MP. - onstruct with a radius viable of 4 arguments cm and a & height of 5 cm. Amy says critique that the the volume reasoning of the of cylinder others. with a radius of 4 cm is double After calculating the volume the volume of the cylinder of both with a radius of 2 cm. She used.4 cylinders, as her ask: value of π. Is she correct? Explain your reasoning. What do you think about what Amy Start by calculating the volume of both predicted? cylinders. (.4)(2) 2 (5) Do you V agree? = Why or (.4)(4)2 (5) Why not? 62.8 cm 25.2 cm click click the question. No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples. click Math Practice Find the Volume Slide / 97 Slide () / 97 Teachers: Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides. Teachers: MP.5 - Use appropriate tools Use this Mathematical Practice strategically. Pull Tab for the next 9 SMART Response Ask: slides. an you make a model to show that? Math Practice Would it help to create a diagram/draw a picture?
9 Slide 2 / 97 Slide 2 () / 97 Find the Volume. Find the Volume. 7 5 in 4 in 2 in 7 5 in VOLUME: 7.2 x (Area in of ase) x 4 (Height) 4.2 in 2 in VOLUME: h 7.2(.5)(4) [This V object = is 4.2 a pull tab] in Slide / 97 2 Find the volume of a rectangular prism with length 2 cm, width. cm and height 5. cm. Slide () / 97 2 Find the volume of a rectangular prism with length 2 cm, width. cm and height 5. cm. VOLUME: h 2(.)(5.) (6.6)(5.).66 cm Slide 4 / 97 Which is a possible length, width and height for a rectangular prism whose volume = 8 cm Slide 4 () / 97 Which is a possible length, width and height for a rectangular prism whose volume = 8 cm A x 2 x 8 A x 2 x 8 6 x x 6 x x 2 x x D x x 2 x x D x x
10 4 Find the volume. 50 ft 47 ft 2 ft Slide 5 / ft Slide 5 () / 97 4 Find the volume. h & = bh of the triangle 2 50 ft 47 V ft= (2)(42)(50) 2 (882)(50) 2 44(50) 22,050 ft 2 ft 42 ft Slide 6 / 97 Slide 6 () / 97 5 A box-shaped refrigerator measures 2 by 0 by 7 on the outside. All six sides of the refrigerator are unit thick. What is the inside volume of the refrigerator in cubic units? 5 A box-shaped refrigerator measures 2 by 0 by 7 on the outside. All six sides of the refrigerator are unit thick. What is the inside volume of the refrigerator in cubic units? HINT: You may want to draw a picture! HINT: You may want to draw a picture! 0 in. 2 in. 8 in. 0 in. 5 in. 7 in. Slide 7 / 97 6 Find the volume. Use.4 as your value of π. 0 m Slide 7 () / 97 6 Find the volume. Use.4 as your value of π. 0 m d = 0 m, so r = 5 m 6 m r 2 h 6 m m
11 Slide 8 / 97 7 Which circular glass holds more water? A Glass A having a 7.5 cm diameter and standing 2 cm high Glass having a 4 cm radius and a height of.5 cm Note: Use.4 as your value of π. Slide 8 () / 97 7 Which circular glass holds more water? Glass A Glass A having a 7.5 cm diameter and A d = 7.5, so r =.75 standing 2 V cm = high h r 2 h.4 (.75) Glass having a 4 cm radius 2 2 and a height of.5 cm cm Glass h r Note: Use.4 as your value 2 h of π..4 (4) cm Slide 9 / 97 8 What is the volume of the largest cylinder that can be placed into a cube that measures 0 feet on an edge? Use.4 as your value of π. Slide 9 () / 97 8 What is the volume of the largest cylinder that can be placed into a cube that measures 0 feet on an edge? Use.4 as your value of π. d = 0 ft, so r = 5 ft & h = 0 ft π (5 2 )(0) π(25)(0) 785 ft Slide 40 / 97 9 A circular garden has a diameter of 20 feet and is surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use.4 as your value of π. Slide 40 () / 97 9 A circular garden has a diameter of 20 feet and is surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use.4 as your value of π. d inner = 20, so r inner = 0 ft r outer = 0 + = ft h = πr 2 h [π( 2 ) - π(0 2 )] (0.5) (69π - 00π)(0.5) (26.66)(0.5) 08. ft
12 Slide 4 / 97 in Terms of π Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers. Slide 42 / 97 Find the Volume Leave your answer in terms of π. 9 yd Ex: If a cylinder has a radius of and a height of 4, then Volume = π() 2 (4) = π(9)(4) = 6π units 2 0 yd Let's try some more problems like this one. lick here to return to cones & spheres. Slide 42 () / 97 Find the Volume Leave your answer in terms of π. Slide 4 / 97 Find the Volume Leave your answer in terms of π. 9 yd 0 yd VOLUME: h r 2 h yd 5 ft 0 ft 5 ft Slide 4 () / 97 Leave your answer in terms of π. Find the Volume 0 ft d = 5, so r = 7.5 VOLUME: h r 2 h (7.5) ft Slide 44 / A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π. A 4π units 28π units 49π units D 98π units
13 Slide 44 () / A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π. Slide 45 / 97 2 A cylinder has a diameter of 2 in. and a height of 2 in. What is its volume? Leave your answer in terms of π. A 4π units 28π units 49π units D 98π units h π (7) 2 2 π πunits D A 44π in 42π in 864π in D,728π in Slide 45 () / 97 2 A cylinder has a diameter of 2 in. and a height of 2 in. What is its volume? Leave your answer in terms of π. Slide 46 / A cylinder has a diameter of 7 in. and a height of 5 in. What is its volume? Leave your answer in terms of π. A 44π in 42π in 864π in D,728π in d = 2 in., so r = 6 in. h π (6) 2 2 π π in A 06.25π in 6.25π in 425π in D,228.25π in Slide 46 () / A cylinder has a diameter of 7 in. and a height of 5 in. What is its volume? Leave your answer in terms of π. A 06.25π in 6.25π in 425π in D,228.25π in d = 7 in., so r = 8.5 in. h π (8.5) 2 5 π πin Slide 47 / 97 2 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π. A 88π ft 76π ft 400π ft D 576π ft
14 Slide 47 () / 97 2 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π. pool: d = 40 ft, so r = 20 ft A 88π ft deck: r = = 24 ft ( π(24) 2 - π(20) 2 )(0.5) 76π ft (576 π- 400 π) π(0.5) 88 ft 400π π ft A D 576π ft Slide 48 / 97 Volume of Pyramids, ones & Spheres Return to Table of ontents Slide 49 / 97 Slide 49 () / 97 Slide 50 / 97 Demonstration comparing volume of ones & Spheres with volume of ylinders click to go to web site A cone is / the volume of a cylinder with the same base area () and height (h). Slide 5 / 97 Volume of a one Area of ase x Height click to reveal (Area of ase x Height) = = h h
15 Slide 52 / 97 Volume of a Sphere Slide 52 () / 97 Volume of a Sphere A sphere is 2/ the volume of a cylinder with the same base area () and height (h). click to reveal 2/ (Volume of ylinder) π V= 2/ ( r 2 h ) or 4/ πr A sphere is 2/ the volume of a cylinder with the same base area () and height (h). Figure click to reveal 2/ (Volume of ylinder) π V= 2/ ( r 2 h ) or 4/ πr Slide 5 / 97 Volume How much ice cream can a Friendly s Waffle cone hold if it has a diameter of 6 in and its height is 0 in? Use.4 as your value of π. (Just Ice ream within one. Not on Top) Volume and Mass used in portion control. $$$ & Math Practice Slide 5 () / 97 Volume (.4)( 2 )(0) How much ice cream can a Friendly s Waffle cone hold if it has a diameter of 6 in and its height is 0 in? Use.4 as 92. in your value of π. Questions to address MP.: (Just What Ice information ream within are one. you given? Not on Top) Volume What and is this Mass problem used asking? portion control. $$$ Questions to address MP.4: Write a number sentence to model this problem. What connections do you see? Slide 54 / Find the volume. Use.4 as your value of π. 9 in 4 in Slide 54 () / Find the volume. Use.4 as your value of π. 9 in 4 in h (π4 2 )(9) (6π)(9) (50.24) in
16 Slide 55 / Find the Volume. Use.4 as your value of π. 5 cm 8 cm Slide 55 () / Find the Volume. Use.4 as your value of π. 8 cm h (π5 2 )(8) 5 cm (25π)(8) (200π) 209 cm Slide 56 / 97 Volume If the radius of a sphere is 5.5 cm, what is its volume? Use.4 as your value of π. Slide 57 / What is the volume of a sphere with a radius of 8 ft? Use.4 as your value of π. lick here 4 πr 4 (.4)(5.5) cm Slide 57 () / What is the volume of a sphere with a radius of 8 ft? Use.4 as your value of π. Slide 58 / What is the volume of a sphere with a diameter of 4.25 in? Use.4 as your value of π. 4 πr 4 (.4)(8) 2,4.57 ft
17 Slide 58 () / What is the volume of a sphere with a diameter of 4.25 in? Use.4 as your value of π. d = 4.25, so r = πr 4 (.4)(2.25) 40.7 in Slide 59 / 97 Volume in Terms of π Similar to when we found the volume of a cylinder, with a cone and a sphere, you could be asked to "Leave your answer in terms of π". lick here if you need to review that property. Slide 60 / 97 You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π. 8 cm Volume in Terms of π cm Slide 60 () / 97 Volume in Terms of π You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your d answer = 8 cm, in so terms r = of 4 π. cm π (4) 2 () 8 cm π(6)() 76 πcm = 58.6 πcm cm Slide 6 / 97 Volume in Terms of π If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π. Slide 6 () / 97 Volume in Terms of π If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π. 4 π(6) 4 π(26) 864 πcm 288 πcm
18 Slide 62 / Find the volume of the cone below. Leave your answer in terms of π. Slide 62 () / Find the volume of the cone below. Leave your answer in terms of π. A 2π in 6π in 48π in D 44π in 9 in 4 in A 2π in 6π in 48π in D 44π in π(4) 2 (9) 9 in π(6)(9) π(6)() 48 πin 4 in Slide 6 / 97 Slide 6 () / Find the volume of the sphere that has a diameter of 8 cm. Leave your answer in terms of π. A 729π cm 972π cm 5,82π cm D 7,776π cm 29 Find the volume of the sphere that has a diameter of 8 cm. Leave your answer in terms of π. d = 8 cm, so r = 9 cm A 729π cm 4 π(9) 972π cm 4 π(729) 5,82π cm 296 π D 7,776π cm 972 π cm Slide 64 / 97 0 Find the volume of the cone below. Leave your answer in terms of π. Slide 64 () / 97 0 Find the volume of the cone below. Leave your answer in terms of π. A 49π in 84π in 47π in D 252π in 7 in 2 in d = 7 in., so r =.5 in. A 49π in π(.5) 2 (2) 84π in π(2.25)(2) 47π in π(2.25)(4) D 252π in49 πin A 7 in 2 in
19 Slide 65 / 97 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π. A 27π cm 9.25π cm 2.5π cm D 64.5π cm Slide 65 () / 97 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π. 4 π(4.5) A 27π cm 4 π(9.25) 9.25π V cm = 64.5π 2.5π V cm= 2.5 πcm D 64.5π cm Slide 66 / 97 2 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 8 cm. Jeff says that the volume of the sphere with a radius of 8 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "". Slide 66 () / 97 2 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 8 cm. Jeff says that the volume of the sphere with a radius of 8 cm is double the volume of V the = 4 sphere π(9) with V a = 4 radius π(8) of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your 4 answer, π(729) type V in = the 4 πnumber (5,82)"". 2,96π 972 π cm 2,28 π 7,776 π cm 7,776 πis not double the volume of 972 π. It's 8 times bigger. Slide 67 / 97 Volume of a Pyramid Slide 68 / 97 Pyramids A pyramid is / the volume of a prism with the same base area () and height (h). Area of ase x Height click to reveal (Area of ase x Height) = = h h Pyramids are named by the shape of their base.. The volume is a pyramid is / the volume of a prism with the same base area() and height (h). h =5 m side length = 4 m h (4)(4)(5) (80) 26 2 m lick here
20 Slide 69 / 97 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 0 in. 0 in Slide 69 () / 97 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 0 in. h [ (4)(8)](0) 2 [ (2)](0) 2 (6)(0) 0 in 5 in 4 in 8 in 4 in 8 in Slide 70 / 97 Slide 70 () / 97 4 Find the volume. 4 Find the volume. h 5. cm V 5. = (8)(7)(5.) cm (56)(5.) 7 cm cm 7 cm 8 cm 8 cm Slide 7 / 97 Slide 72 / 97 5 Find the volume. More Practice / Review 22 mm 8 mm 5 mm Return to Table of ontents
21 5 Find the volume. 5 mm Slide 72 () / mm h V 8 mm = (5)(8)(22) 880 mm Slide 7 / 97 6 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of. meters, and the height of the pyramid is 2.4 meters. HINT: Drawing a diagram will help! Slide 7 () / 97 6 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of. meters, and the height of the pyramid is 2.4 meters. Slide 74 / 97 7 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of inches. HINT: Drawing a diagram will help! h (2.7)(.)(2.4) m Slide 74 () / 97 Slide 75 / 97 7 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of inches. 8 Find the Volume. h (4 2 )() 6 in 2 m m 6 m 9 m 9 m
22 8 Find the Volume. Slide 75 () / 97 Slide 76 / 97 9 Find the Volume. Use.4 as your value of π. 9 m h [ (9)(6)]() 2 (27)() m 99 m 2 m 6 m 9 m 4 ft 2 ft Slide 76 () / 97 9 Find the Volume. Use.4 as your value of π. Slide 77 / Find the Volume. Use.4 as your value of π. h π(7 2 )(2) 2 ft (.4)(49)(2), ft 4 ft 6.9 in 8 in Slide 77 () / 97 Slide 78 / Find the Volume. Use.4 as your value of π. 4 Find the Volume. h π(4 2 )(6.9) 8 in (.4)(6)(6.9) V 6.9 = in in 4 ft 9 ft 8 ft 7 ft
23 Slide 78 () / 97 Slide 79 / 97 4 Find the Volume. 9 ft 42 A cone 20 cm in diameter and 4 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter? 4 ft 8 ft h 7(4) (8) 2 V= 2 ft 20 cm 4 cm 7 ft 25 cm Slide 79 () / 97 Slide 80 / A cone 20 cm in diameter and 4 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter? one ube /(.4)(0 20 cm )(4) cm 5625 cm 5625/ cm# 0.7 about cones 25 cm 4 Find the Volume. 9 in 2 in 8 in 7 in 9 in 4 Find the Volume. Slide 80 () / 97 Slide 8 / 97 Name a -D Figure that is not a polyhedron. 9 in 2 in 7 in 8 in 9 in h 7(2) (8) 2 V= 56 in
24 Slide 8 () / 97 Name a -D Figure that is not a polyhedron. Slide 82 / 97 Name a -D figure that has 6 rectangular faces. possible answers cylinder cone Slide 82 () / 97 Slide 8 / 97 Name a -D figure that has 6 rectangular faces. 44 Find the volume. 70 m rectangular prism 80 m 40 m 44 Find the volume. Slide 8 () / 97 Slide 84 / The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height. 80 m 70 m h 80(40)(70) 40 m 224,000 m Part A: What is the volume of the cone, in cubic feet? A 2π ft 6π ft 6π ft D 48π ft From PAR EOY sample test calculator #
25 Slide 84 () / The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height. Slide 85 / Part : What is the ratio of the cone's volume to the cylinder's volume? π(4) 2 () π(6)() π(6) Part A: What is the V volume = 6 πft of the cone, in cubic feet? A 2π ft 6π ft 6π ft D 48π ft From PAR EOY sample test calculator # Slide 85 () / 97 Slide 86 / Part : What is the ratio of the cone's volume to the cylinder's volume? one: 6 πft 6π Ratio = = 48π ylinder: π(4) 2 () π(6)() 48 π ft Glossary & Standards Return to Table of ontents Slide 86 () / 97 Slide 87 / 97 one Teacher Notes Glossary & Standards Vocabulary Words are bolded in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it. Return to Table of ontents A polyhedron that has one circular base with a vertex opposite of it and sides that are curved. curved surface polyhedron ice cream cone pencil tip traffic cone ack to Instruction
26 Slide 88 / 97 ylinder Slide 89 / 97 Edge A polyhedron that has two congruent circular bases which are parallel to one another and sides that are curved. Line segment formed where 2 faces meet. curved surface polyhedron candles pizza Pringles can A triangular pyramid has 6 edges. ack to Instruction ack to Instruction Slide 90 / 97 Euler's Formula The number of edges plus 2 is equal to the sum of the faces and vertices. E + 2 = F + V Slide 9 / 97 Face Flat surface of a polyhedron. pyramid: vertices = 4 faces = 4 E + 2= F + V E + 2 = E + 2 = 8 E = 6 A triangular pyramid has 4 faces. (there is one you can't see) ack to Instruction ack to Instruction Slide 92 / 97 Polyhedron A -D figure whose faces are all polygons. Slide 9 / 97 Prism A polyhedron that has two congruent, polygon bases which are parallel to one another, sides that are rectangular, and named by the shape of their base. ubes Prisms Pyramids Made of: Faces Edges Vertices ylinders ones Rectangular Prism Pentagonal Prism Triangular Pris m juice box body of pencil lock of cheese ack to Instruction ack to Instruction
27 Slide 94 / 97 Pyramid Slide 95 / 97 Vertex A polyhedron that has one polygon base with a vertex opposite of it,sides that are triangular, and named by the shape of its base. Point where two or more straight lines/ faces/edges meet. A orner. Triangular Pyramid Square Pyramid Pentagonal Pyramid A triangular pyramid has 4 vertices. ack to Instruction ack to Instruction Slide 96 / 97 Volume The amount of space occupied by a D figure. The number of cubic units needed to fill a D figure (layering). Slide 97 / 97 Standards for Mathematical Practices MP Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP onstruct viable arguments and critique the reasoning of others. MP4 Model with mathematics. volume of prisms and cylinders: area of base x height area of base x h 2m x 5m x 8m 80m Label: Units or cubic units MP5 Use appropriate tools strategically. MP6 Attend to precision. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. ack to Instruction lick on each standard to bring you to an example of how to meet this standard within the unit.
8th Grade. Slide 1 / 97. Slide 2 / 97. Slide 3 / 97. 3D Geometry. Table of Contents. 3-Dimensional Solids. Volume. Glossary & Standards
Slide 1 / 97 Slide 2 / 97 8th Grade 3D Geometry 2015-11-20 www.njctl.org Table of Contents Slide 3 / 97 3-Dimensional Solids Click on the topic to go to that section Volume Prisms and Cylinders Pyramids,
More informationFebruary 07, Dimensional Geometry Notebook.notebook. Glossary & Standards. Prisms and Cylinders. Return to Table of Contents
Prisms and Cylinders Glossary & Standards Return to Table of Contents 1 Polyhedrons 3-Dimensional Solids A 3-D figure whose faces are all polygons Sort the figures into the appropriate side. 2. Sides are
More information3 Dimensional Solids. Table of Contents. 3 Dimensional Solids Nets Volume Prisms and Cylinders Pyramids, Cones & Spheres
Table of Contents 3 Dimensional Solids Nets Volume Prisms and Cylinders Pyramids, Cones & Spheres Surface Area Prisms Pyramids Cylinders Spheres More Practice/ Review 3 Dimensional Solids Polyhedron A
More information3 Dimensional Geometry Chapter Questions. 1. What are the differences between prisms and pyramids? Cylinders and cones?
3 Dimensional Geometry Chapter Questions 1. What are the differences between prisms and pyramids? Cylinders and cones? 2. What is volume and how is it found? 3. How are the volumes of cylinders, cones
More informationPractice A Introduction to Three-Dimensional Figures
Name Date Class Identify the base of each prism or pyramid. Then choose the name of the prism or pyramid from the box. rectangular prism square pyramid triangular prism pentagonal prism square prism triangular
More informationGEOMETRY. slide #3. 6th Grade Math Unit 7. 6th Grade Unit 7: GEOMETRY. Name: Table of Contents. Area of Rectangles
Name: 6th Grade Math Unit 7 GEOMETRY 2012 10 17 www.njctl.org 1 Table of Contents Area of Rectangles Area of Parallelograms Area of Triangles Area of Trapezoids Mixed Review Area of Irregular Figures Area
More informationLesson 10T ~ Three-Dimensional Figures
Lesson 10T ~ Three-Dimensional Figures Name Period Date Use the table of names at the right to name each solid. 1. 2. Names of Solids 3. 4. 4 cm 4 cm Cone Cylinder Hexagonal prism Pentagonal pyramid Rectangular
More informationSect Volume. 3 ft. 2 ft. 5 ft
199 Sect 8.5 - Volume Objective a & b: Understanding Volume of Various Solids The Volume is the amount of space a three dimensional object occupies. Volume is measured in cubic units such as in or cm.
More information2nd Grade. 2D Shapes - Part 1 Angles and Sides. Slide 1 / 117 Slide 2 / 117. Slide 3 / 117. Slide 4 / 117. Slide 6 / 117.
Slide 1 / 117 Slide 2 / 117 2nd Grade Geometry Presentation 1 2015-11-30 www.njctl.org Slide 3 / 117 Table of ontents Presentation 1 2 Shapes - Sides and ngles - Part 1 2 Shapes - Part 2 Lab: 2 Shapes
More information6th Grade. Slide 1 / 219. Slide 2 / 219. Slide 3 / 219. Geometry. Table of Contents
Slide 1 / 219 Slide 2 / 219 6th Grade Geometry 2015-12-01 www.njctl.org Table of Contents Area of Rectangles Click on a topic to Area of Parallelograms go to that section Area of Right Triangles Area of
More information3. Draw the orthographic projection (front, right, and top) for the following solid. Also, state how many cubic units the volume is.
PAP Geometry Unit 7 Review Name: Leave your answers as exact answers unless otherwise specified. 1. Describe the cross sections made by the intersection of the plane and the solids. Determine if the shape
More information422 UNIT 12 SOLID FIGURES. The volume of an engine s cylinders affects its power.
UNIT 12 Solid Figures The volume of an engine s cylinders affects its power. 422 UNIT 12 SOLID FIGURES Gas-powered engines are driven by little explosions that move pistons up and down in cylinders. When
More informationVocabulary. Triangular pyramid Square pyramid Oblique square pyramid Pentagonal pyramid Hexagonal Pyramid
CP1 Math 2 Unit 8: S.A., Volume, Trigonometry: Day 7 Name Surface Area Objectives: Define important vocabulary for 3-dimensional figures Find the surface area for various prisms Generalize a formula for
More informationUnit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon
Unit 7: 3D Figures 10.1 & 10.2 2D formulas & Area of Regular Polygon NAME Name the polygon with the given number of sides: 3-sided: 4-sided: 5-sided: 6-sided: 7-sided: 8-sided: 9-sided: 10-sided: Find
More informationVolume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth.
Volume of Cylinders As with prisms, the area of the base of a cylinder tells the number of cubic units in one layer. The height tells how many layers there are in the cylinder. The volume V of a cylinder
More informationPage 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D 2D & 3D GEOMETRY PERIMETER/CIRCUMFERENCE & AREA SURFACE AREA & VOLUME
Page 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D UNIT 9 2016-17 2D & 3D GEOMETRY PERIMETER/CIRCUMFERENCE & AREA SURFACE AREA & VOLUME CCM6+7+ Name: Math Teacher: Projected Test Date: MAIN CONCEPT(S) PAGE(S) Vocabulary
More information6th Grade. Geometry.
1 6th Grade Geometry 2015 12 01 www.njctl.org 2 Table of Contents Area of Rectangles Area of Parallelograms Area of Right Triangles Area of Acute and Obtuse Triangles Area of Trapezoids Mixed Review Area
More informationGeometry Solids Identify Three-Dimensional Figures Notes
26 Geometry Solids Identify Three-Dimensional Figures Notes A three dimensional figure has THREE dimensions length, width, and height (or depth). Intersecting planes can form three dimensional figures
More informationSection 9.4. Volume and Surface Area. Copyright 2013, 2010, 2007, Pearson, Education, Inc.
Section 9.4 Volume and Surface Area What You Will Learn Volume Surface Area 9.4-2 Volume Volume is the measure of the capacity of a three-dimensional figure. It is the amount of material you can put inside
More informationPart I Multiple Choice
Oregon Focus on Surface Area and Volume Practice Test ~ Surface Area Name Period Date Long/Short Term Learning Targets MA.MS.07.ALT.05: I can solve problems and explain formulas involving surface area
More informationMeasurement 1 PYTHAGOREAN THEOREM. The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of
Measurement 1 PYTHAGOREAN THEOREM Remember the Pythagorean Theorem: The area of the square on the hypotenuse of a right triangle is equal to the sum of the areas of the squares on the other two sides.
More informationGeometry 10 and 11 Notes
Geometry 10 and 11 Notes Area and Volume Name Per Date 10.1 Area is the amount of space inside of a two dimensional object. When working with irregular shapes, we can find its area by breaking it up into
More informationPage 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D. Angle Relationships, Area, and Perimeter/Circumference Surface Area and Volume
Page 1 CCM6+7+ UNIT 9 GEOMETRY 2D and 3D UNIT 9 2015-16 Angle Relationships, Area, and Perimeter/Circumference Surface Area and Volume CCM6+7+ Name: Math Teacher: Projected Test Date: MAIN CONCEPT(S) PAGE(S)
More informationName: Target 12.2: Find and apply surface of Spheres and Composites 12.2a: Surface Area of Spheres 12.2b: Surface Area of Composites Solids
Unit 12: Surface Area and Volume of Solids Target 12.0: Euler s Formula and Introduction to Solids Target 12.1: Find and apply surface area of solids 12.1a: Surface Area of Prisms and Cylinders 12.1b:
More informationVocabulary. Term Page Definition Clarifying Example. cone. cube. cylinder. edge of a threedimensional. figure. face of a polyhedron.
CHAPTER 10 Vocabulary The table contains important vocabulary terms from Chapter 10. As you work through the chapter, fill in the page number, definition, and a clarifying example. cone Term Page Definition
More informationNotes: Geometry (6.G.1 4)
Perimeter Add up all the sides (P =s + s + s...) Square A = side 2 A = S 2 Perimeter The distance around a polygon. Rectangle w s L A = Length x Width A = lw Parallelogram A = Base x Height A = h h Triangle
More informationACCELERATED MATHEMATICS CHAPTER 11 DIMENSIONAL GEOMETRY TOPICS COVERED:
ACCELERATED MATHEMATICS CHAPTER DIMENSIONAL GEOMETRY TOPICS COVERED: Naming 3D shapes Nets Volume of Prisms Volume of Pyramids Surface Area of Prisms Surface Area of Pyramids Surface Area using Nets Accelerated
More informationReteaching. Solids. These three-dimensional figures are space figures, or solids. A cylinder has two congruent circular bases.
9- Solids These three-dimensional figures are space figures, or solids A B C D cylinder cone prism pyramid A cylinder has two congruent circular bases AB is a radius A cone has one circular base CD is
More informationChapter 7. Description or Example. Found on Page. Vocabulary Term. Definition. base. center. circumference. chord. complex figure. cone.
C H A P T E R 7 This is an alphabetical list of new vocabulary terms you will learn in Chapter 7. As you complete the study notes for the chapter, you will see Build Your Vocabulary reminders to complete
More informationGrades 7 & 8, Math Circles 20/21/22 February, D Geometry Solutions
Faculty of Mathematics Waterloo, Ontario NL 3G1 Centre for Education in Mathematics and Computing D Geometry Review Grades 7 & 8, Math Circles 0/1/ February, 018 3D Geometry Solutions Two-dimensional shapes
More informationDraw and Classify 3-Dimensional Figures
Introduction to Three-Dimensional Figures Draw and Classify 3-Dimensional Figures Identify various three-dimensional figures. Course 2 Introduction to Three-Dimensional Figures Insert Lesson Title Here
More informationUnit 3: 2D and 3D Measurement & Optimizing Measurements ISU
MPM 1DE NAME: Unit 3: D and 3D Measurement & Optimizing Measurements ISU To complete this independent study, you are required to fill in the appropriate information where necessary, work through the given
More informationMATH-8 Review Volume of 3D shapes 2018 N Exam not valid for Paper Pencil Test Sessions
MATH-8 Review Volume of 3D shapes 2018 N Exam not valid for Paper Pencil Test Sessions [Exam ID:2YBSPT 1 What is the volume of a cube with a length of 8 inches? A 96 in 3 B 256 in 3 C 512 in 3 D 384 in
More informationMath 8: Identify Shapes and Surface Area
Name: Class: Date: Math 8: Identify Shapes and Surface Area 1. Name the solid according to its description: The figure has one base that is a rectangle and four lateral surfaces that are triangles. 2.
More informationJunior Math Circles March 3, D Geometry I
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Junior Math Circles March 3, 2010 3D Geometry I Opening Problem Max received a gumball machine for his
More informationS8.6 Volume. Section 1. Surface area of cuboids: Q1. Work out the surface area of each cuboid shown below:
Things to Learn (Key words, Notation & Formulae) Complete from your notes Radius- Diameter- Surface Area- Volume- Capacity- Prism- Cross-section- Surface area of a prism- Surface area of a cylinder- Volume
More informationUNIT 12. Volume and Surface Area CCM6+ Name: Math Teacher: Projected Test Date: Vocabulary 2. Basics of 3-D Figures 3 8
UNIT 12 Volume and Surface Area 2016 2017 CCM6+ Name: Math Teacher: Projected Test Date: Main Concept(s) Page(s) Vocabulary 2 Basics of 3-D Figures 3 8 Volume of Rectangular Prisms and Finding Missing
More informationSolid Figures. Name. 22 Topic 18. Reteaching Polyhedrons Prisms
Solid Figures Polyhedrons Prisms Pyramids Reteaching 8- Properties of polyhedrons include vertices, edges, and faces, and base(s). Square Pyramid K Reteaching 8- Not Polyhedrons Cylinder Cone Sphere H
More informationSEVENTH EDITION and EXPANDED SEVENTH EDITION
SEVENTH EDITION and EXPANDED SEVENTH EDITION Slide 9-1 Chapter 9 Geometry 9.1 Points, Lines, Planes, and Angles Basic Terms A line segment is part of a line between two points, including the endpoints.
More informationNumber/Computation. addend Any number being added. digit Any one of the ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
14 Number/Computation addend Any number being added algorithm A step-by-step method for computing array A picture that shows a number of items arranged in rows and columns to form a rectangle associative
More informationUnit 5. Area & Volume. Area Composite Area Surface Area Volume. Math 6 Unit 5 Calendar 1/14 1/15 1/16 1/17 1/18. Name: Math Teacher:
Math 6 Unit 5 Calendar 1/14 1/15 1/16 1/17 1/18 Name: Unit 5 Area & Volume Area Composite Area Surface Area Volume Review Or Computer Lab Unit 5 Test Or Computer Lab Unit 5 Test Or Computer Lab Unit 5
More informationLesson 9. Three-Dimensional Geometry
Lesson 9 Three-Dimensional Geometry 1 Planes A plane is a flat surface (think tabletop) that extends forever in all directions. It is a two-dimensional figure. Three non-collinear points determine a plane.
More informationAdditional Practice. Name Date Class
Additional Practice Investigation 1 1. The four nets below will fold into rectangular boxes. Net iii folds into an open box. The other nets fold into closed boxes. Answer the following questions for each
More informationMath 6: Geometry 3-Dimensional Figures
Math 6: Geometry 3-Dimensional Figures Three-Dimensional Figures A solid is a three-dimensional figure that occupies a part of space. The polygons that form the sides of a solid are called a faces. Where
More informationPre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume
Pre-Algebra Notes Unit 0: Geometric Figures & Their Properties; Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (4.6) The student will validate conclusions about geometric figures and
More informationGrades 7 & 8, Math Circles 20/21/22 February, D Geometry
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing 2D Geometry Review Grades 7 & 8, Math Circles 20/21/22 February, 2018 3D Geometry Two-dimensional shapes
More informationMATH-8 Review Surface Area 3D 2018 N Exam not valid for Paper Pencil Test Sessions
MATH-8 Review Surface Area 3D 2018 N Exam not valid for Paper Pencil Test Sessions [Exam ID:J42YVD 1 What is the surface area of the rectangular prism shown? A 48 cm 2 B 24 cm 2 C 52 cm 2 D 26 cm 2 2 A
More informationPYRAMIDS AND CONES WHAT YOU LL LEARN. Ø Finding the surface areas and volume of pyramids Ø Finding the surface areas and volume of cones
PYRAMIDS AND CONES A pyramid is a solid with a polygonal base and triangular lateral faces that meet at a vertex. In this lesson, you will work with regular pyramids. The base of a regular pyramid is a
More informationSomeone else might choose to describe the closet by determining how many square tiles it would take to cover the floor. 6 ft.
Areas Rectangles One way to describe the size of a room is by naming its dimensions. So a room that measures 12 ft. by 10 ft. could be described by saying its a 12 by 10 foot room. In fact, that is how
More informationUnit 8 Syllabus: Surface Area & Volume
Date Period Day Unit 8 Syllabus: Surface Area & Volume Topic 1 Space Figures and Cross Sections Surface Area and Volume of Spheres 3 Surface Area of Prisms and Cylinders Surface Area of Pyramids and Cones
More information4.1 Exploring Nets (pp )
Math 8 Unit 4 Notes Name: 4.1 Exploring Nets (pp. 170-176) Net: a pattern that can be folded to make an object Ex. Polyhedron: an object with faces that are polygons Prism: an object that has two congruent
More informationFree Response. Test A. 1. What is the estimated area of the figure?
Test A 1. What is the estimated area of the 6. An 8.5 in. by 11 in. sheet of paper is enlarged to make a poster by doubling its length and width. What is the new perimeter? 7. How does the area of a square
More informationLesson 4: Volumes of Pyramids and Cones
: Volumes of Pyramids and Cones Learning Targets I can calculate the volumes of pyramids. I can apply the properties of right triangles and trigonometry to find the volume of pyramids Volumes of pyramids
More informationMy Notes CONNECT TO SCIENCE. Horticulture is the science and art of growing fruit, flowers, ornamental plants, and vegetables.
SUGGESTED LEARNING STRATEGIES: Summarize/Paraphrase/ Retell, Use Manipulatives, Activating Prior Knowledge, Self/ Peer Revision The Horticulture Club has been given some land to build a greenhouse. The
More informationThe Geometry of Solids
CONDENSED LESSON 10.1 The Geometry of Solids In this lesson you will Learn about polyhedrons, including prisms and pyramids Learn about solids with curved surfaces, including cylinders, cones, and spheres
More informationAssignment Guide: Chapter 11 Geometry (L3)
Assignment Guide: Chapter 11 Geometry (L3) (136) 11.1 Space Figures and Cross Sections Page 692-693 #7-23 odd, 35 (137) 11.2/11.4 Surface Areas and Volumes of Prisms Page 703-705 #1, 2, 7-9, 11-13, 25,
More informationGeometry Review Chapter 10: Volume PA Anchors: A3; B2; C1. 1. Name the geometric solid suggested by a frozen juice can.
Geometry Review Chapter 10: Volume PA Anchors: A; B2; C1 1. Name the geometric solid suggested by a frozen juice can. 2. Name the geometric solid suggested by a beach ball.. Name the geometric solid suggested
More information12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.
Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have
More information11.4 Three-Dimensional Figures
11. Three-Dimensional Figures Essential Question What is the relationship between the numbers of vertices V, edges E, and faces F of a polyhedron? A polyhedron is a solid that is bounded by polygons, called
More informationGeometry: Notes
Geometry: 11.5-11.8 Notes NAME 11.5 Volumes of Prisms and Cylinders Date: Define Vocabulary: volume Cavalieri s Principle density similar solids Examples: Finding Volumes of Prisms 1 Examples: Finding
More informationPre-Algebra, Unit 10: Measurement, Area, and Volume Notes
Pre-Algebra, Unit 0: Measurement, Area, and Volume Notes Triangles, Quadrilaterals, and Polygons Objective: (4.6) The student will classify polygons. Take this opportunity to review vocabulary and previous
More informationTo find the surface area of a pyramid and a cone
11-3 Surface Areas of Pyramids and Cones Common Core State Standards G-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects. MP 1, MP 3, MP 4, MP 6, MP 7 Objective To find
More informationacute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6
acute angle An angle with a measure less than that of a right angle. Houghton Mifflin Co. 2 Grade 5 Unit 6 angle An angle is formed by two rays with a common end point. Houghton Mifflin Co. 3 Grade 5 Unit
More informationLesson 14.1 Skills Practice
Lesson 14.1 Skills Practice Name Date Cut, Fold, and Voila! Nets Vocabulary Define each term in your own words. 1. geometric solids 2. net 3. prototype 4. edge 5. face 6. vertex Problem Set Sketch and
More informationAttendance Questions: Find the area of each shape. Round your answer to the nearest tenth. 1. An equilateral triangle with edge length 20 cm.
Page 1 of 17 Attendance Questions: Find the area of each shape. Round your answer to the nearest tenth. 1. An equilateral triangle with edge length 20 cm. Page 1 of 17 Page 2 of 17 2. A regular hexagon
More informationGeometry Vocabulary. acute angle-an angle measuring less than 90 degrees
Geometry Vocabulary acute angle-an angle measuring less than 90 degrees angle-the turn or bend between two intersecting lines, line segments, rays, or planes angle bisector-an angle bisector is a ray that
More informationKansas City Area Teachers of Mathematics 2018 KCATM Math Competition
Kansas City Area Teachers of Mathematics 2018 KCATM Math Competition GEOMETRY AND MEASUREMENT TEST GRADE 6 #51-90 INSTRUCTIONS Do not open this booklet until instructed to do so. Time limit: 20 minutes
More informationWrite Euler s Theorem. Solving Problems Using Surface Area and Volume. Figure Surface Area Volume. Cl V 5 1 } 3
CHAPTER SUMMARY Big Idea 1 BIG IDEAS Exploring Solids and Their Properties For Your Notebook Euler s Theorem is useful when finding the number of faces, edges, or vertices on a polyhedron, especially when
More informationUNIT 3 - MEASUREMENT & PROPORTIONAL REASONING TEST
Class: Date: UNIT 3 - MEASUREMENT & PROPORTIONAL REASONING TEST Multiple Choice Identify the choice that best completes the statement or answers the question. 1. When designing a building, you must be
More informationUnit 3 Surface Area and Volume
Name: 3.1 Areas of 2D Figures 3.2 Surface Areas of Prisms and Pyramids 3.3 Surface Areas of Cylinders, Cones and Spheres 3.4 Volumes of Prisms and Pyramids 3.5 Volumes of Cylinders, Cones and Spheres 3.1
More informationC in. 2. D in Find the volume of a 7-inch tall drinking glass with a 4-inch diameter. C lateral faces. A in. 3 B in.
Standardized Test A For use after Chapter Multiple Choice. Which figure is a polyhedron? A B 7. Find the surface area of the regular pyramid. A 300 ft 2 B 340 ft 2 C 400 ft 2 C D D 700 ft 2 2. A polyhedron
More informationCourse 1 Unit 5 Practice
Course Unit Practice Lesson -. Attend to precision. Use the Triangle Inequality Property to determine whether a triangle can be formed with the given side lengths in inches. If a triangle can be formed,
More informationChapter 12 Review Period:
Chapter 12 Review Name: Period: 1. Find the number of vertices, faces, and edges for the figure. 9. A polyhedron has 6 faces and 7 vertices. How many edges does it have? Explain your answer. 10. Find the
More informationReady To Go On? Skills Intervention 10-1 Solid Geometry
10A Find these vocabulary words in Lesson 10-1 and the Multilingual Glossary. Vocabulary Ready To Go On? Skills Intervention 10-1 Solid Geometry face edge vertex prism cylinder pyramid cone cube net cross
More informationLesson 22: Surface Area
Student Outcomes Students find the surface area of three-dimensional objects whose surface area is composed of triangles and quadrilaterals, specifically focusing on pyramids. They use polyhedron nets
More informationMathematics Assessment Anchor Glossary Grades 3 & 4
Mathematics Assessment Anchor Glossary Grades 3 & 4 The definitions for this glossary were taken from one or more of the following sources: Webster s Dictionary, various mathematics dictionaries, the PA
More informationL22 Measurement in Three Dimensions. 22a Three Dimensions Warmup
22a Three Dimensions Warmup Let s take a look at two-dimensional and three-dimensional objects below. A vertex (plural: vertices) (#VOC) in a 2 or 3-dimensional object is a point where two or more straight
More informationPolygons. 5 sides 5 angles. pentagon. no no R89. Name
Lesson 11.1 Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number of angles
More informationMATH-G P- Geometry Formulas Exam not valid for Paper Pencil Test Sessions
MATH-G P- Geometry Formulas Exam not valid for Paper Pencil Test Sessions [Exam ID:2M8EKV 1 A soda can has a diameter of 6 centimeters and a height of 13 centimeters. Which is closest to the surface area
More information1.4 Surface Area of Right Pyramids and Right Cones
Math 1201 Date: 1.4 Surface Area of Right Pyramids and Right Cones Understanding how to calculate surface area can be helpful in many real world applications. For example, surface area can be used to estimate
More informationVolume review. 1. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches.
Name: ate: 1. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. 3. Which diagram represents the figure with the greatest volume? A.... What is the volume
More informationLesson 1 - Area Review Shape Words Formula
Lesson 1 - Area Review Shape Words Formula Rectangle The area A of a rectangle is the product of the length and the width w. A = w Parallelogram The area A of a parallelogram is the product of any base
More informationPolygons. 5 sides 5 angles. pentagon. Name
Lesson 11.1 Reteach Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number
More informationHS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume
HS Pre-Algebra Notes Unit 0: Measurement, Area, and Volume Triangles, Quadrilaterals, and Polygons Syllabus Objectives: (5.6) The student will classify polygons. (5.5) The student will validate conclusions
More informationGeometry Surface Area & Volume of Prisms & Cylinders.
Geometry 11.5 Surface Area & Volume of Prisms & Cylinders mbhaub@mpsaz.org 11.5 Essential Question How do you find the surface area and volume of a prism or cylinder? Geometry 12.2 Surface Area of Prisms
More informationThe radius for a regular polygon is the same as the radius of the circumscribed circle.
Perimeter and Area The perimeter and area of geometric shapes are basic properties that we need to know. The more complex a shape is, the more complex the process can be in finding its perimeter and area.
More informationName: Period 3/23/12 4/12/12 Pre-AP
Name: Period 3/23/12 4/12/12 Pre-AP UNIT 14: SOLIDS I can define, identify and illustrate the following terms: Face Edge Vertex Cross section Prism Height Surface area Lateral surface area Net Volume Scale
More informationSurface Area and Volume
Surface Area and Volume Day 1 - Surface Area of Prisms Surface Area = The total area of the surface of a three-dimensional object (Or think of it as the amount of paper you ll need to wrap the shape.)
More informationUnit 4 End-of-Unit Assessment Study Guide
Circles Unit 4 End-of-Unit Assessment Study Guide Definitions Radius (r) = distance from the center of a circle to the circle s edge Diameter (d) = distance across a circle, from edge to edge, through
More informationCCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li
CCM6+ Unit 12 Surface Area and Volume page 1 CCM6+ UNIT 12 Surface Area and Volume Name Teacher Kim Li MAIN CONCEPTS Page(s) Unit 12 Vocabulary 2 3D Figures 3-8 Volume of Prisms 9-19 Surface Area 20-26
More information6.G.1. SELECTED RESPONSE Select the correct answer. CONSTRUCTED RESPONSE. 3. What is the area of this shape?
6.G.1 SELECTED RESPONSE Select the correct answer. 3. What is the area of this shape? 1. What is the area of the triangle below? 5.65 cm 10.9375 cm 11.5 cm 1.875 cm 48 in 144 in 96 in 88 in 4. What is
More informationLesson Polygons
Lesson 4.1 - Polygons Obj.: classify polygons by their sides. classify quadrilaterals by their attributes. find the sum of the angle measures in a polygon. Decagon - A polygon with ten sides. Dodecagon
More informationCHAPTER 12. Extending Surface Area and Volume
CHAPTER 12 Extending Surface Area and Volume 0 Learning Targets Students will be able to draw isometric views of three-dimensional figures. Students will be able to investigate cross-sections of three-dimensional
More information7 th Grade CCGPS Math LFS Unit 5: Geometry
7 th Grade CCGPS Math LFS Unit 5: Geometry Standards: Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. MCC7.G.2 (DOK2) Draw (freehand, with ruler
More informationGeometry Unit 10 Note Sheets Date Name of Lesson. 1.6 Two-Dimensional Figures Areas of Circles and Sectors
Date Name of Lesson 1.6 Two-Dimensional Figures 11.3 Areas of Circles and Sectors Quiz 11.1 Areas of Parallelograms and Triangles 11.2 Areas of Trapezoids, Rhombi and Kites 11.4 Areas of Regular Polygons
More informationTest Chapter 11. Matching
Test Chapter 11 Matching Match each vocabulary term with its definition. a. cube b. cylinder c. cone d. sphere e. prism f. pyramid g. hemisphere 1. a polyhedron formed by a polygonal base and triangular
More information11.4 Volume of Prisms and Cylinders
11.4 Volume of Prisms and Cylinders Learning Objectives Find the volume of a prism. Find the volume of a cylinder. Review Queue 1. Define volume in your own words. 2. What is the surface area of a cube
More informationLesson 11-1 Three-Dimensional Figures Lesson 11-2 Volume: Prisms and Cylinders Lesson 11-3 Volume: Pyramids, Cones, and Spheres Lesson 11-4 Surface
Lesson 11-1 Three-Dimensional Figures Lesson 11-2 Volume: Prisms and Cylinders Lesson 11-3 Volume: Pyramids, Cones, and Spheres Lesson 11-4 Surface Area: Prisms and Cylinders Lesson 11-5 Surface Area:
More informationVolume of Prisms and Cylinders
Name Date Teacher Practice A Volume of Prisms and Cylinders Find the volume of each figure to the nearest tenth of a unit. Prism: V = Bh. Cylinder: V = π 2 r h. Use 3.14 for π. 1. 2. 3. 4. 5. 6. 7. 8.
More informationRectangular prism. The two bases of a prism. bases
Page 1 of 8 9.1 Solid Figures Goal Identify and name solid figures. Key Words solid polyhedron base face edge The three-dimensional shapes on this page are examples of solid figures, or solids. When a
More information