Slide / 97 Slide 2 / 97 8th Grade D Geometry 205--20 www.njctl.org 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
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
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
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 6 8 2 Rectangular Prism Triangular Prism Triangular Pyramid Square Pyramid Pentagonal Pyramid Octagonal Prism 6 8 2 5 6 9 4 4 6 5 5 8 6 6 0 0 6 24 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.
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
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
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 http://njctl.org/courses/ 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) 5 2 8 x 8 (Height) 0 8 80 m 80 m
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.4 254.4 x 0 (Height) 254.4 yd (Area of ase) VOLUME: h r 2 h.4 9 2 0.4 8 0 254.4 0 254.4 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?
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.5 0.8 4 (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
4 Find the volume. 50 ft 47 ft 2 ft Slide 5 / 97 42 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.4 5 2 6.4 25 6 78.5 6 47 m
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.4 4.0625 2 of.5 cm 529.875 cm Glass h r Note: Use.4 as your value 2 h of π..4 (4) 2.5.4 6.5 577.76 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
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 9 2 0 8 0 80 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) 2 0 56.25 0 687.5 ft Slide 44 / 97 20 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
Slide 44 () / 97 20 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 49 2 98 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 / 97 22 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 6 2 42 π in A 06.25π in 6.25π in 425π in D,228.25π in Slide 46 () / 97 22 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 72.25 5 6.25 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
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 = 20 + 4 = 24 ft ( π(24) 2 - π(20) 2 )(0.5) 76π ft (576 π- 400 π)0.5 76 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
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 / 97 24 Find the volume. Use.4 as your value of π. 9 in 4 in Slide 54 () / 97 24 Find the volume. Use.4 as your value of π. 9 in 4 in h (π4 2 )(9) (6π)(9) (50.24) 50.72 in
Slide 55 / 97 25 Find the Volume. Use.4 as your value of π. 5 cm 8 cm Slide 55 () / 97 25 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 / 97 26 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) 696.6 cm Slide 57 () / 97 26 What is the volume of a sphere with a radius of 8 ft? Use.4 as your value of π. Slide 58 / 97 27 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
Slide 58 () / 97 27 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 = 2.25 4 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
Slide 62 / 97 28 Find the volume of the cone below. Leave your answer in terms of π. Slide 62 () / 97 28 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 () / 97 29 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
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
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 285.6 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
5 Find the volume. 5 mm Slide 72 () / 97 22 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) 2.808 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
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 / 97 40 Find the Volume. Use.4 as your value of π. h π(7 2 )(2) 2 ft (.4)(49)(2),077.02 ft 4 ft 6.9 in 8 in Slide 77 () / 97 Slide 78 / 97 40 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 5.552 in 4 ft 9 ft 8 ft 7 ft
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 / 97 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? one ube /(.4)(0 20 cm )(4) 25 465. cm 5625 cm 5625/465. 4 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
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 / 97 45 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 #
Slide 84 () / 97 45 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 / 97 46 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 / 97 46 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
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 = 4 + 4 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
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.