How can the surface area of a three-dimensional figure be determined?

Size: px
Start display at page:

Download "How can the surface area of a three-dimensional figure be determined?"

Transcription

1 1.3 Surface Area Consider the groceries in the photograph. What three-dimensional geometric figures do you recognize? Is it a coincidence that so many packages are in these shapes? Think about: the cost of materials the cost of shipping storage and shelving displays The surface area of a three-dimensional figure is an important consideration in package design. Investigate Tools variety of boxes and cans (with labels) scissors ruler net a two-dimensional pattern that can be folded to make a threedimensional object How can the surface area of a three-dimensional figure be determined? Part A Surface Area of a Rectangular-Based Prism 1. Choose a box that is in the shape of a rectangle-based prism. Measure its length l, width, w, and height, h. 2. a) Carefully cut along the edges of the box so that you can lay it flat. This is called a net. b) Count the number of faces in the net. What are the shapes of the faces? c) Identify pairs of congruent faces. Label each face with its dimensions. 26 MHR Chapter 1 01_FFCM12_CH1.indd 26 3/6/09 12:17:27 PM

2 3. a) Calculate the area of each face. b) Add the areas to determine the surface area of the box. 4. Reflect The surface area of a rectangular-based prism can be expressed using the formula S.A. = 2(lw + wh + hl). Explain how the formula relates to the net. Part B Surface Area of a Cylinder 1. a) Choose a cylindrical can. Measure the diameter, d, and height, h, of the cylinder. b) Determine the radius diameter, d of the cylinder. 2. a) Carefully remove the label from the can and lay it flat. b) What is the shape of the label? c) How are the dimensions of the label related to the dimensions of the can? height, h lateral face surface of a threedimensional object that is not a base 3. a) Calculate the areas of the top and bottom of the cylinder. b) Calculate the area of the lateral face of the cylinder. This is equal to the area of the label. c) Determine the surface area of the cylinder. 4. Reflect The surface area of a cylinder can be expressed using the formula S.A. = 2πr 2 + 2πrh. Explain how the formula relates to the components of the cylinder. 1.3 Surface Area MHR 27 01_FFCM12_CH1.indd 27 3/6/09 12:17:28 PM

3 Example 1 Cylindrical Packaging A tennis ball has a diameter of 67 mm. A cylindrical container holds three stacked tennis balls. Determine the amount of material required for the container to the nearest square centimetre. Solution The container is a cylinder with a diameter of 67 mm and height of 3 67, or 201 mm. A = 2 (πr 2 ) 201 mm A = 2πrh 67 mm Determine the radius. r = d 2 = 67 2 = 33.5 The radius of the cylinder is 33.5 mm. Substitute r = 33.5 and h = 201 into the formula for the surface area of a cylinder. Be sure to follow the correct order of operations. S.A. = 2πr 2 + 2πrh = 2π(33.5) 2 + 2π(33.5)(201) 2 π 33.5 x π = = = The surface area of the container is mm 2. Convert the surface area from square millimetres to square centimetres. Since m = 1 cm, 10 2 mm 2 = 1 2 cm 2. Divide by 10 2 or = The surface area of the cylindrical container is approximately 494 cm MHR Chapter 1 01_FFCM12_CH1.indd 28 3/6/09 12:17:28 PM

4 Example 2 Surface Area of a Composite Figure A riser is a raised platform used on a stage. This riser, for a rock performance, is to be painted. 12 m 6 m 16 m Determine the surface area to be painted. Do not include the bottom of the riser. Solution Sketch a net showing the top, front, back, and side faces of the riser. Side Back Top Front 12 m 6 m x Side 16 m Calculate the area of each face and then add the areas to determine the total surface area to be painted. Top The top is a rectangle with dimensions of 12 m by. A Top = lw = (12)(10) = 120 The area of the top is 120 m 2. Back The back is a rectangle with dimensions of 12 m 6 m. A Back = lw = (12)(6) = 72 The area of the back is 72 m Surface Area MHR 29 01_FFCM12_CH1.indd 29 3/6/09 12:17:29 PM

5 Sides The sides are in the shape of a trapezoid. Method 1: Use components. Divide the trapezoid into a rectangle and a triangle. 6 m 6 m 6 m 16 m 16 m - = 6m Add the areas of the rectangular and triangular components. A Side = lw + 1 _ 2 bh = (10)(60) + 1 _ 2 (6)(6) = = 78 Method 2: Apply the area of a trapezoid formula. 6 m The area of each side of the riser is 78 m m A Side = _ 1 (a + b)h 2 = _ 1 ( )6 2 = 78 Front The front is a rectangle, with one dimension unknown. This edge is the same length as the slanted edge of the trapezoid-shaped side. The yellow shape is a right triangle. Use the Pythagorean theorem. x 2 = x 2 = m x 2 = 72 x m The length of the edge is approximately 8.5 m. Determine the area of the front of the riser. A Front = lw (12)(8.5) 102 The area of the front is approximately 102 m 2. Add the areas of the faces to determine the surface area of the riser. S.A. = A Top + A Back + 2A Side + A Front Remember to include the areas = (78) of the two trapezoidal sides. = 450 The total surface area to be painted is approximately 450 m 2. x 30 MHR Chapter 1 01_FFCM12_CH1.indd 30 3/6/09 12:17:29 PM

6 Key Concepts The surface area of a three-dimensional figure is the sum of the areas of all of its outer faces, measured in square units. A net is a two-dimensional model that shows the faces of a threedimensional figure. Nets are useful for counting and identifying the shapes of the faces. Discuss the Concepts D1. a) How does the surface area of a box change if you remove the top? S.A. = 2(lw + wh + hl) S.A. = b) Explain your answer to part a) using words and a formula. D2. a) How does the surface area of a cylinder change if you remove the top? S.A. = 2 (πr 2 ) + 2πrh S.A. = b) Explain your answer to part a) using words and a formula. D3. Consider this triangular-based prism. a) How many faces are there? b) What shapes are the faces? c) How many congruent pairs of faces are there? Identify their shapes. d) Explain how you could find the surface area of this figure. 1.3 Surface Area MHR 31 01_FFCM12_CH1.indd 31 3/6/09 12:17:29 PM

7 Practise A 1. a) Draw a net for this photograph box. 6 cm 15 cm 12 cm b) Determine the surface area of the box. 2. Refer to question 1. Suppose the lid was removed from the box. a) Show how this would change the net. b) Determine the surface area of the new box. 3. This bookend is in the shape of a triangular-based prism. Draw the net and then determine the surface area of the bookend. 20 cm 15 cm Apply B 4. A hockey puck has a height of 1 in. and a diameter of 3 in. Draw the net then determine the surface area of the puck, to the nearest square inch. 5. A can of coconut juice has dimensions as shown. Determine the surface area of the can to the nearest square centimetre. 6 cm Reasoning and Proving 18 cm Representing Selecting Tools Problem Solving Connecting Reflecting Communicating 32 MHR Chapter 1 6. Refer to question 5. Calculate the minimum surface area of a box with a lid that could hold 12 cans, arranged in 3 rows of 4 cans. 01_FFCM12_CH1.indd 32 3/6/09 12:17:30 PM

8 7. Determine the outer surface area of a cylindrical vase with a radius of 12 cm and a height of 0.50 m to the nearest hundredth of a square metre. Assume there is no lid. 8. A golf ball has a diameter of 40 mm. Determine the minimum surface area of a square-based prism that will hold two golf balls. 40 mm 9. Refer to question 8. a) Determine the surface area of the square-based prism that is just large enough to hold 16 golf balls stacked in a 4 by 4 arrangement, as shown. b) Which requires less packaging, 8 boxes of 2 balls each or 1 box of 16 balls? Why does this make sense? Technology Tip Do not change the scale on the axes or your area measurements will be incorrect. 10. Refer to Example 2. a) Use The Geometer s Sketchpad to draw a net for the riser. b) Construct polygon interiors for the various shapes and find their areas. c) Determine the total surface area of the riser. d) Compare your answer to the one found in the Example. How close are they? 1.3 Surface Area MHR 33 01_FFCM12_CH1.indd 33 3/6/09 12:17:31 PM

9 Reasoning and Proving Representing Selecting Tools Problem Solving Connecting Reflecting Communicating Achievement Check 11. Kate needs to purchase a new liner for the outdoor pool at the local community centre. 18 m 36 m 4 m 1.5 m 20 m a) Determine the surface area of the liner required to cover the bottom, front, back, and sides of the pool, to the nearest square metre. Explain the steps in your solution. b) The material for the liner costs $5 per square metre. Determine the cost of material for this liner. Do you think this represents the total cost? What other costs might be involved? 12. Recall Fido s doghouse from section m Fido 2.0 m 1.0 m 1.4 m a) What is the surface area of the exterior of the doghouse before the doorway is cut? Include the floor. b) The exterior walls and roof of Fido s house are to be painted. A 40-cm wide doorway has been cut as shown. The doorway is 60 cm at its highest point. What is the area to be painted? 34 MHR Chapter 1 01_FFCM12_CH1.indd 34 3/6/09 12:17:31 PM

10 Chapter Problem 13. Next to the skiers lanes on Horstman Glacier is the terrain park for snowboarders and freestyle skiers. r 100 m Extend C Your friend tells you that it took three bags of salt to cover the surface area of the 100-m long half-pipe shown. Recall that each bag of salt can cover 400 m 2 of snow. a) Determine the surface area of the half-pipe. b) Determine the depth of the half-pipe. 14. A cylindrical wheel of cheese is divided into six congruent sectorbased prisms, as shown. 20 cm 8 cm What is the least amount of wrapping required for each wedge of cheese? 15. Refer to question 9, part a). Design a box with a smaller surface area that will hold 16 golf balls in a different arrangement. Sketch the new box and label its dimensions. 16. The cylindrical walls of an open-top silo have an outside diameter of 5.0 m, a thickness of 50 cm, and a height of. A can of paint covers 12 m 2, and costs $ How much will it cost to paint the silo, including the inside, the outside, and the top of the walls? 1.3 Surface Area MHR 35 01_FFCM12_CH1.indd 35 3/6/09 12:17:32 PM

Surface Area and Volume

Surface 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 information

17.2 Surface Area of Prisms

17.2 Surface Area of Prisms h a b c h a b c Locker LESSON 17. Surface Area of Prisms and Cylinders Texas Math Standards The student is expected to: G.11.C Apply the formulas for the total and lateral surface area of three-dimensional

More information

My Notes CONNECT TO SCIENCE. Horticulture is the science and art of growing fruit, flowers, ornamental plants, and vegetables.

My 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 information

19.2 Surface Area of Prisms and Cylinders

19.2 Surface Area of Prisms and Cylinders Name Class Date 19. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Resource Locker Explore Developing a Surface Area Formula Surface

More information

Volume of Cylinders. Volume of Cones. Example Find the volume of the cylinder. Round to the nearest tenth.

Volume 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 information

Identify the following 3-D Geometric Shapes

Identify the following 3-D Geometric Shapes 5.1 Intro January 3, 2011 4:55 PM Identify the following 3-D Geometric Shapes Important Terms Chapter 5 Page 1 - - - - - Face: Any flat area on a prism Curved Area: The curved part of a cylinder or cone

More information

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry Solutions

Grades 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 information

Grades 7 & 8, Math Circles 20/21/22 February, D Geometry

Grades 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 information

8.3. Surface Area and Volume of Prisms and Pyramids. Investigate

8.3. Surface Area and Volume of Prisms and Pyramids. Investigate 8.3 Surface Area and Volume of Prisms and Pyramids surface area the number of square units needed to cover the surface of a three-dimensional object volume the amount of space that an object occupies,

More information

Unit 7: 3D Figures 10.1 & D formulas & Area of Regular Polygon

Unit 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 information

Unit 3: 2D and 3D Measurement & Optimizing Measurements ISU

Unit 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 information

SP about Rectangular Blocks

SP about Rectangular Blocks 1 3D Measure Outcomes Recognise and draw the nets of prisms, cylinders, and cones. Solve problems about the surface area and volume of rectangular blocks, cylinders, right cones, prisms, spheres, and solids

More information

UNIT 11 VOLUME AND THE PYTHAGOREAN THEOREM

UNIT 11 VOLUME AND THE PYTHAGOREAN THEOREM UNIT 11 VOLUME AND THE PYTHAGOREAN THEOREM INTRODUCTION In this Unit, we will use the idea of measuring volume that we studied to find the volume of various 3 dimensional figures. We will also learn about

More information

3 Dimensional Solids. Table of Contents. 3 Dimensional Solids Nets Volume Prisms and Cylinders Pyramids, Cones & Spheres

3 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 information

UNIT 6 MEASUREMENT AND GEOMETRY - PRACTICE

UNIT 6 MEASUREMENT AND GEOMETRY - PRACTICE UNIT 6 MEASUREMENT AND GEOMETRY - PRACTICE UNIT 6 MEASUREMENT AND GEOMETRY - PRACTICE... 1 PERIMETER AND AREA PROBLEMS... Answers... 3 VOLUME AND SURFACE AREA PROBLEMS... 4 Answers... 5 SOME CHALLENGING

More information

When discussing 3-D solids, it is natural to talk about that solid s Surface Area, which is the sum of the areas of all its outer surfaces or faces.

When discussing 3-D solids, it is natural to talk about that solid s Surface Area, which is the sum of the areas of all its outer surfaces or faces. Lesson 3 Lesson 3, page 1 of 10 Glencoe Geometry Chapter 11. Nets & Surface Area When discussing 3-D solids, it is natural to talk about that solid s Surface Area, which is the sum of the areas of all

More information

MODULE 18 VOLUME FORMULAS

MODULE 18 VOLUME FORMULAS MODULE 18 VOLUME FORMULAS Objectives Use formulas routinely for finding the perimeter and area of basic prisms, pyramids, cylinders, cones, and spheres. Vocabulary: Volume, right vs oblique Assignments:

More information

Lesson 10T ~ Three-Dimensional Figures

Lesson 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 information

1.4 Surface Area of Right Pyramids and Right Cones

1.4 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 information

Pre-Algebra, Unit 10: Measurement, Area, and Volume Notes

Pre-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 information

February 07, Dimensional Geometry Notebook.notebook. Glossary & Standards. Prisms and Cylinders. Return to Table of Contents

February 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 information

422 UNIT 12 SOLID FIGURES. The volume of an engine s cylinders affects its power.

422 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 information

Measurement 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. 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 information

Surface Area of a Cylinder

Surface Area of a Cylinder Surface Area of a Cylinder Focus on After this lesson, you will be able to... find the surface area of a cylinder Glow sticks work because of a chemical reaction. There are two solutions in separate compartments

More information

CC Investigation 4: Measurement

CC Investigation 4: Measurement CC Investigation : Measurement A net is a two-dimensional model that can be folded into a threedimensional figure. Prisms are three-dimensional figures that have two congruent and parallel faces that are

More information

Geometry 10 and 11 Notes

Geometry 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 information

Someone else might choose to describe the closet by determining how many square tiles it would take to cover the floor. 6 ft.

Someone 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 information

Part 1: Perimeter and Area Relationships of a Rectangle

Part 1: Perimeter and Area Relationships of a Rectangle Part 1: Perimeter and Area Relationships of a Rectangle Optimization: the process of finding values that make a given quantity the greatest (or least) possible given certain conditions. Investigation 1:

More information

Volume of Rectangular Prisms and Pyramids. Use the formula. Substitute for l and w. Use the formula. Substitute for B and h.

Volume of Rectangular Prisms and Pyramids. Use the formula. Substitute for l and w. Use the formula. Substitute for B and h. ? LESSON 10.1 ESSENTIAL QUESTION Volume of Rectangular Prisms and Pyramids How do you find the volume of a rectangular prism and a rectangular pyramid? Finding the Volume of a Rectangular Prism Remember

More information

Lesson 10 ~ Three-Dimensional Figures

Lesson 10 ~ Three-Dimensional Figures Lesson 10 ~ Three-Dimensional Figures Name a solid that fits each description. 1. a can of beans 2. a shoe box 3. a pyramid with five lateral faces 4. a solid with six vertices 5. a prism with bases shaped

More information

EMERGENCY SHELTER DESIGN STEM LEARNING AT ITS BEST

EMERGENCY SHELTER DESIGN STEM LEARNING AT ITS BEST KSB * 1 ( * KNOWLEDGE AND SKILL BUILDER) Geometric shapes student Name: Period: school: date: Hofstra University Center for Technological Literacy Simulations and Modeling for Technology Education This

More information

Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets

Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets Name: Surface Area & Volume Packet Engage NY Lesson 15: Representing Three-Dimensional Figures Using Nets Classwork Cereal Box Similarities: Cereal Box Differences: Exercise 1 1. Some of the drawings below

More information

Section 9.4. Volume and Surface Area. Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 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 information

Part I Multiple Choice

Part 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 information

Pythagorean Theorem. Pythagorean Theorem

Pythagorean Theorem. Pythagorean Theorem MPM 1D Unit 6: Measurement Lesson 1 Date: Learning goal: how to use Pythagorean Theorem to find unknown side length in a right angle triangle. Investigate: 1. What type of triangle is in the centre of

More information

Math 10 C Measurement Unit

Math 10 C Measurement Unit Math 10 C Measurement Unit Name: Class: Date: ID: A Chapter Test Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which imperial unit is most appropriate

More information

Geometry Solids Identify Three-Dimensional Figures Notes

Geometry 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 information

Chapter 7. Description or Example. Found on Page. Vocabulary Term. Definition. base. center. circumference. chord. complex figure. cone.

Chapter 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 information

Lesson 1 - Area Review Shape Words Formula

Lesson 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 information

DRAFT CHAPTER. Surface Area GET READY. xxx. Math Link. 5.1 Warm Up xxx. 5.1 Views of Three-Dimensional Objects xxx. 5.

DRAFT CHAPTER. Surface Area GET READY. xxx. Math Link. 5.1 Warm Up xxx. 5.1 Views of Three-Dimensional Objects xxx. 5. CHAPTER 5 Surface Area GET READY Math Link xxx xxx 5.1 Warm Up xxx 5.1 Views of Three-Dimensional Objects xxx 5.2 Warm Up xxx 5.2 Nets of Three-Dimensional Objects xxx 5.3 Warm Up xxx 5.3 Surface Area

More information

HS Pre-Algebra Notes Unit 10: Measurement, Area, and Volume

HS 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 information

To find the surface area of a pyramid and a cone

To 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 information

Write down a formula for the surface area of a Prism and a Cylinder

Write down a formula for the surface area of a Prism and a Cylinder Write down a formula for the surface area of a Prism and a Cylinder Quiz Thursday Naming Figures Cross Sections Nets Lateral Area, Surface Area Prisms and cylinders have 2 congruent parallel bases. A lateral

More information

Determine the surface area of the following square-based pyramid. Determine the volume of the following triangular prism. ) + 9.

Determine the surface area of the following square-based pyramid. Determine the volume of the following triangular prism. ) + 9. MPM 1D Name: Unit: Measurement Date: Calculating and of Three Dimensional Figures Use the Formula Sheet attached to help you to answer each of the following questions. Three problems are worked out for

More information

Volume and Surface Area Unit 28 Remember Volume of a solid figure is calculated in cubic units and measures three dimensions.

Volume and Surface Area Unit 28 Remember Volume of a solid figure is calculated in cubic units and measures three dimensions. Volume and Surface Area Unit 28 Remember Volume of a solid figure is calculated in cubic units and measures three dimensions. Surface Area is calculated in square units and measures two dimensions. Prisms

More information

UNIT 0 MEASUREMENT AND GEOMETRY - PRACTICE

UNIT 0 MEASUREMENT AND GEOMETRY - PRACTICE UNIT 0 MEASUREMENT AND GEOMETRY - PRACTICE UNIT 0 MEASUREMENT AND GEOMETRY - PRACTICE... 1 PERIMETER AND AREA PROBLEMS...... 3 VOLUME AND SURFACE AREA PROBLEMS... 4... 5 SOME CHALLENGING PROBLEMS THAT

More information

11.4 Volume of Prisms and Cylinders

11.4 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 information

Pre-Algebra Notes Unit 10: Geometric Figures & Their Properties; Volume

Pre-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 information

Geometry. Week 32: April 13-17, 2015

Geometry. Week 32: April 13-17, 2015 G.13 Geometry Week 32: April 13-17, 2015 The student will use formulas for surface area and volume of threedimensional objects to solve real-world problems. G.14 The student will use similar geometric

More information

2. A square has a side length of 9 mm. What is the area of the square? A 18 mm² B 36 mm² C 49 mm² D 81 mm²

2. A square has a side length of 9 mm. What is the area of the square? A 18 mm² B 36 mm² C 49 mm² D 81 mm² Chapter 3 Test. BLM 3 18. For #1 to #5, select the best answer. 1. Which number is not a perfect square? A 9 B 16 C 55 D 121 2. A square has a side length of 9 mm. What is the area of the square? A 18

More information

Name: Block Score /36 Version: A

Name: Block Score /36 Version: A Name: _ Block Score /36 Version: A Surface Area & Volume Matching Match the correct term to each of the following descriptions. A term may be used more than once or not at all. a. edge h. net b. face i.

More information

Geometry Surface Area & Volume of Prisms & Cylinders.

Geometry 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 information

Name Date Class Practice A LESSON Surface Area. Find the surface area S of each net Find the surface area S of each prism

Name Date Class Practice A LESSON Surface Area. Find the surface area S of each net Find the surface area S of each prism Practice A Find the surface area S of each net. 1. 2. 3. 4. Find the surface area S of each prism. 5. 6. _ Practice B Find the surface area S of each prism. 1. 2. _ Find the surface area S of each pyramid.

More information

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets): Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:

More information

Chapter 1: Symmetry and Surface Area

Chapter 1: Symmetry and Surface Area Chapter 1: Symmetry and Surface Area Name: Section 1.1: Line Symmetry Line of symmetry(or reflection): divides a shape or design into two parts. Can be found using: A mirra Folding Counting on a grid Section

More information

STAAR Category 3 Grade 7 Mathematics TEKS 7.9D. Student Activity 1

STAAR Category 3 Grade 7 Mathematics TEKS 7.9D. Student Activity 1 Student Activity 1 Work with your partner to answer the following questions. Problem 1: A triangular prism has lateral faces and faces called bases. The bases are in the shape of a. The lateral faces are

More information

UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet

UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet Name Period Date UNIT 4: LENGTH, AREA, AND VOLUME WEEK 16: Student Packet 16.1 Circles: Area Establish the area formula for a circle. Apply the area formula for a circle to realistic problems. Demonstrate

More information

7 th Grade CCGPS Math LFS Unit 5: Geometry

7 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 information

Sect Volume. 3 ft. 2 ft. 5 ft

Sect 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 information

Assignment Guide: Chapter 11 Geometry (L3)

Assignment 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 information

Unit 3 Surface Area and Volume

Unit 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 information

1 Measurement - Nets, Surface Area and Volume. Terms

1 Measurement - Nets, Surface Area and Volume. Terms 1 Measurement - Nets, Surface Area and Volume Terms 2 Measurement - Nets, Surface Area and Volume Nets 1. Draw a net for the following shape. Include all measurements and symbols. 2. 3. 4. 3 Measurement

More information

Math 8: Identify Shapes and Surface Area

Math 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 information

1.0 Fractions Review Name: Date: Goal: to review some key fractions skills in preparation for the upcoming unit. Main Ideas: b)!!

1.0 Fractions Review Name: Date: Goal: to review some key fractions skills in preparation for the upcoming unit. Main Ideas: b)!! 1.0 Fractions Review Name: Date: Goal: to review some key fractions skills in preparation for the upcoming unit Toolkit: Working with integers Operations with fractions Main Ideas: Reducing Fractions To

More information

Volume of Pyramids and Cones

Volume of Pyramids and Cones Volume of Pyramids and Cones Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content, visit

More information

UNCORRECTED PAGE PROOFS

UNCORRECTED PAGE PROOFS TOPIC 5 Surface area and volume 5.1 Overview 5.1.1 Introduction If we re able to calculate the surface area of shapes, we re able to know the amount of fabric we need to make a tent or how much paint we

More information

Surface Area of a Prism

Surface Area of a Prism Surface Area of a Prism Focus on After this lesson, you will be able to... link area to surface area find the surface area of a right prism Most products come in some sort of packaging. You can help conserve

More information

Chapter 1 Measurement

Chapter 1 Measurement Chapter 1 Measurement Math 1201 1 Chapter 1 Measurement Sections 1.1-1.3: Goals: Converting between imperial units by unit analysis Converting between SI units Converting between SI and imperial units

More information

AREA OF POLYGONS

AREA OF POLYGONS AREA OF POLYGONS 5.3.1 5.3.4 Area is the number of non-overlapping square units needed to cover the interior region of a twodimensional figure or the surface area of a three-dimensional figure. For example,

More information

Vocabulary. Triangular pyramid Square pyramid Oblique square pyramid Pentagonal pyramid Hexagonal Pyramid

Vocabulary. 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 information

Surface Area of Triangular Prisms - Nets

Surface Area of Triangular Prisms - Nets U2B L6: Students will determine the surface area of a triangular prism Surface Area of Triangular Prisms - Nets Surface area - the area of all the faces of the prism Triangular prism - made up of three

More information

CCM6+ 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 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 information

12-4 Volumes of Prisms and Cylinders. Find the volume of each prism.

12-4 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 information

Aptitude Volume and Surface Area. Theory

Aptitude Volume and Surface Area. Theory Aptitude Volume and Surface Area Theory Volume Volume is the amount of space inside a three-dimensional (length, width and height.) object, or its capacity. measured in cubic units. Surfce Area Total area

More information

Surface Area of Prisms and Cylinders

Surface Area of Prisms and Cylinders Surface Area of Prisms and Cylinders Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,

More information

Lesson 9. Three-Dimensional Geometry

Lesson 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 information

#1 A: Surface Area of Triangular Prisms Calculate the surface area of the following triangular prisms. You must show ALL of your work.

#1 A: Surface Area of Triangular Prisms Calculate the surface area of the following triangular prisms. You must show ALL of your work. #1 A: Surface Area of Triangular Prisms Calculate the surface area of the following triangular prisms. You must show ALL of your work. (a) (b) (c) (d) (e) #1 B: VOLUME of Triangular Prisms Calculate the

More information

The radius for a regular polygon is the same as the radius of the circumscribed circle.

The 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 information

Measurement Unit. This booklet belongs to:

Measurement Unit. This booklet belongs to: Measurement Unit This booklet belongs to: LESSON # DATE QUESTIONS FROM NOTES 1 2 3 4 5 6 7 8 Questions to review This booklet is homework and will be collected on the test day. Your teacher has important

More information

Teacher Page. 1. Find the surface area of the prism. a. 315 in 2 b. 630 in 2 c. 450 in 2 d. 820 in 2

Teacher Page. 1. Find the surface area of the prism. a. 315 in 2 b. 630 in 2 c. 450 in 2 d. 820 in 2 Teacher Page Geometry / Day #12 Surface Area 45 Minutes 9-12.G.1.3 Draw three-dimensional objects and calculate the surface areas and volumes of these figures (e.g. prisms, cylinders, pyramids, cones,

More information

Additional Practice. Name Date Class

Additional 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 information

Copy the squares below onto 1-cm grid paper.

Copy the squares below onto 1-cm grid paper. Project Making Squares into Cubes Part 1 Copy the squares below onto 1-cm grid paper. Materials 1-cm grid paper wooden or plastic cubes ruler 1-cm grid card stock scissors tape Determine the area of each

More information

Practice A Introduction to Three-Dimensional Figures

Practice 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 information

Math 10 Lesson 6 4 Surface Area of Pyramids and Cones

Math 10 Lesson 6 4 Surface Area of Pyramids and Cones Math 0 esson 6 4 Surface Area of Pyramids and Cones I. esson Objectives: ) Solve problems involving the surface areas of right pyramids and right cones. II. Surface area of a right pyramid A right pyramid

More information

Perimeter, Area, Surface Area, & Volume

Perimeter, Area, Surface Area, & Volume Additional Options: Hide Multiple Choice Answers (Written Response) Open in Microsoft Word (add page breaks and/or edit questions) Generation Date: 11/25/2009 Generated By: Margaret Buell Copyright 2009

More information

Surface Area of Solids

Surface Area of Solids Lesson 24 Surface Area of Solids Name: Prerequisite: Use a Net to Find Surface Area Study the example showing how to use a net to find the surface area of a prism. Then solve problems 7. Example Kioshi

More information

Algebra/Geometry Institute Summer 2010

Algebra/Geometry Institute Summer 2010 Algebra/Geometry Institute Summer 2010 Faculty Name: Diana Sanders School: John F. Kennedy Memorial High School Mound Bayou, MS Grade Level: 7 th Grade Investigating Surface Area 1. Teaching objective(s)

More information

Chapter 2 Self-Assessment

Chapter 2 Self-Assessment Chapter 2 Self-Assessment. BLM 2 1 Concept BEFORE DURING (What I can do) AFTER (Proof that I can do this) 2.1 I can use linear units to convert area and volume units within the SI system. I can use linear

More information

Reteaching. Solids. These three-dimensional figures are space figures, or solids. A cylinder has two congruent circular bases.

Reteaching. 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 information

Lesson 24: Surface Area

Lesson 24: Surface Area Student Outcomes Students determine the surface area of three-dimensional figures, those that are composite figures and those that have missing sections. Lesson Notes This lesson is a continuation of Lesson

More information

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets): Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:

More information

Math 6: Geometry 3-Dimensional Figures

Math 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 information

Date Lesson Text TOPIC Homework. Angles in Triangles Pg. 371 # 1-9, 11, 14, 15. CBR/Distance-Time Graphs Pg. 392 # 3, 4, 5, 7, 8

Date Lesson Text TOPIC Homework. Angles in Triangles Pg. 371 # 1-9, 11, 14, 15. CBR/Distance-Time Graphs Pg. 392 # 3, 4, 5, 7, 8 UNIT 7 THE REST! Date Lesson Text TOPIC Homework May 22 7.1 9.2 May 23 7.2 9.3 May 24 7.3 9.4 Optimization Rectangles Optimization Square-Based Prism Optimization Cylinder WS 7.1 Pg. 495 # 2, 3, 5a, 7

More information

Area and Volume 2. Circles. Trapeziums. and Measures. Geometry. Key Point. Key Point. Key Point

Area and Volume 2. Circles. Trapeziums. and Measures. Geometry. Key Point. Key Point. Key Point Geometry and Measures Area and Volume 2 You must be able to: Recall and use the formulae for the circumference and area of a circle Recall and use the formula for the area of a trapezium Recall and use

More information

Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms & Cylinders (12.2)

Unit 9: Solid Geometry Lesson 3: Surface Area of Prisms & Cylinders (12.2) Unit 9: Solid Geometry Lesson 3: Surface rea of Prisms & ylinders (12.2) Learning Targets: 9I raw the net of a prism, and use it to develop a formula for the surface area of a right prism. 9K erive the

More information

The Geometry of Solids

The 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 information

11.5 Start Thinking Warm Up Cumulative Review Warm Up

11.5 Start Thinking Warm Up Cumulative Review Warm Up 11.5 Start Thinking Consider the stack of coins shown in Figure A. What is the volume of the cylinder formed by the stack of coins? The same coins are stacked as shown in Figure B. What is the volume of

More information

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets):

Park Forest Math Team. Meet #5. Self-study Packet. Problem Categories for this Meet (in addition to topics of earlier meets): Park Forest Math Team Meet #5 Self-study Packet Problem Categories for this Meet (in addition to topics of earlier meets): 1. Mystery: Problem solving 2. : Solid (Volume and Surface Area) 3. Number Theory:

More information

Answer Key: Three-Dimensional Cross Sections

Answer Key: Three-Dimensional Cross Sections Geometry A Unit Answer Key: Three-Dimensional Cross Sections Name Date Objectives In this lesson, you will: visualize three-dimensional objects from different perspectives be able to create a projection

More information

Students construct nets of three dimensional objects using the measurements of a solid s edges.

Students construct nets of three dimensional objects using the measurements of a solid s edges. Student Outcomes Students construct nets of three dimensional objects using the measurements of a solid s edges. Lesson Notes In the previous lesson, a cereal box was cut down to one of its nets. On the

More information