Solve Problems Using DiagramsUse diagrams to solve measurement problems.

116 Chapter 11: Geometry and Measurement Relationships Copyright © 2006 by Nelson Education Ltd.

1. Find the volume of each figure.

a)

b)

2. Calculate the surface area of the figure below.

At-Home HelpWhen you are given a complexproblem to solve, try breaking upthe problem into smaller parts.For example, if you are asked tofind the volume of a complexshape, start by dividing the shapeinto simpler parts. Sketch eachpart separately. Find the volumeof each part, then add themtogether to find the total volume.

3 cm

4 cm

7 cm

5 cm

3 cm

3 cm

2 cm

4 cm2 cm

2 cm2 cm

10 cm

6 cm

3 cm15 cm

10 cm

11-Math8WB-CH11 7/27/10 10:21 AM Page 116

Goal

cube octahedron

dodecahedrontetrahedronicosahedron

Copyright © 2006 by Nelson Education Ltd. Chapter 11: Geometry and Measurement Relationships 117

1. The five Platonic solids are shown on this page, alongwith their nets. Fill out the table below to describesome of the properties of these solids. Some of thetable has been filled in for you.

Exploring the Platonic SolidsInvestigate properties of the Platonic solids.

At-Home HelpA polyhedron is a 3-D shape thathas polygons as its faces.

A regular polygon is a polygonthat has all sides equal and allangles equal.

A Platonic solid is a polyhedronwith faces that are all congruentregular polygons. There are onlyfive Platonic solids. Platonicsolids can be made fromequilateral triangles, squares, andregular pentagons.

Number of Number of Number of Number of Type of faces vertices edges faces (at

Polyhedron polygon (in total) (in total) (in total) each vertex)

Tetrahedron triangle Octahedron 4Icosahedron 20 30CubeDodecahedron 20 30

11-Math8WB-CH11 7/27/10 10:21 AM Page 117

Goal

Copyright © 2017 by Nelson Education Ltd. Geometry and Measurement Relationships 117

9780176823405_M_WB_G8_P3.indd 117 10/01/17 2:21 PM

Polyhedron Faces, Edges, andVertices

Determine how the number of faces, edges, and vertices of a polyhedronare related.

118 Chapter 11: Geometry and Measurement Relationships Copyright © 2006 by Nelson Education Ltd.

1. A polyhedron has 6 faces and 4 vertices. Use Euler’sformula to calculate the number of edges.

2. A polyhedron has 12 vertices and 22 edges. UseEuler’s formula to calculate the number of faces.

3. Show that Euler’s formula works for each polyhedron.

a) c)

b) d)

4. Tran says he is building a polyhedron with 5 vertices, 14 edges, and11 faces. Benjamin says, “That’s not possible.” Who is correct? Why?

At-Home HelpThe number of faces, edges, andvertices of a polyhedron arerelated. Euler’s formula describesthis relationship: F � V � E � 2,where F is the number of faces, V is the number of vertices, and E is the number of edges of thepolyhedron.

11-Math8WB-CH11 7/27/10 10:21 AM Page 118

Goal

Copyright © 2006 by Nelson Education Ltd. Chapter 11: Geometry and Measurement Relationships 119

1. Calculate the surface area of eachcylinder.

a)

b)

c)

d)

2. Use the net to find the surface area ofthe cylinder.

3. A cylinder has a radius of 15.5 cm and aheight of 7.5 cm. Calculate the surfacearea.

4. Estimate which cylinder has thegreatest volume.

5. A circular swimming pool has adiameter of 7.4 m, and a height of2.4 m. What is the volume of the pool?

Test Yourself

10 cm

15 cm

2.2 cm

3.3 cm

2.8 cm

1.5 cm

8.0 cm

8.0 cm

4 cm

9 cm

12 cm

20 cm

7 cmA

9 cm

B

11-Math8WB-CH11 7/27/10 10:21 AM Page 119

118 Geometry and Measurement Relationships Copyright © 2017 by Nelson Education Ltd.

9780176823405_M_WB_G8_P3.indd 118 10/01/17 2:21 PM

Polyhedron Faces, Edges, andVertices

Determine how the number of faces, edges, and vertices of a polyhedronare related.

118 Chapter 11: Geometry and Measurement Relationships Copyright © 2006 by Nelson Education Ltd.

1. A polyhedron has 6 faces and 4 vertices. Use Euler’sformula to calculate the number of edges.

2. A polyhedron has 12 vertices and 22 edges. UseEuler’s formula to calculate the number of faces.

3. Show that Euler’s formula works for each polyhedron.

a) c)

b) d)

4. Tran says he is building a polyhedron with 5 vertices, 14 edges, and11 faces. Benjamin says, “That’s not possible.” Who is correct? Why?

At-Home HelpThe number of faces, edges, andvertices of a polyhedron arerelated. Euler’s formula describesthis relationship: F � V � E � 2,where F is the number of faces, V is the number of vertices, and E is the number of edges of thepolyhedron.

11-Math8WB-CH11 7/27/10 10:21 AM Page 118

Goal

Copyright © 2006 by Nelson Education Ltd. Chapter 11: Geometry and Measurement Relationships 119

1. Calculate the surface area of eachcylinder.

a)

b)

c)

d)

2. Use the net to find the surface area ofthe cylinder.

3. A cylinder has a radius of 15.5 cm and aheight of 7.5 cm. Calculate the surfacearea.

4. Estimate which cylinder has thegreatest volume.

5. A circular swimming pool has adiameter of 7.4 m, and a height of2.4 m. What is the volume of the pool?

Test Yourself

10 cm

15 cm

2.2 cm

3.3 cm

2.8 cm

1.5 cm

8.0 cm

8.0 cm

4 cm

9 cm

12 cm

20 cm

7 cmA

9 cm

B

11-Math8WB-CH11 7/27/10 10:21 AM Page 119

Copyright © 2017 by Nelson Education Ltd. Geometry and Measurement Relationships 119

9780176823405_M_WB_G8_P3.indd 119 10/01/17 2:21 PM

Study Planner

Sunday Monday Tuesday Wednesday Thursday Friday Saturday

Study Topic Checklist

Number Relationships Proportional Relationships Collecting, Organizing, and Displaying Data

Patterns and Relationships Measurement of Circles Integer Operations Transformations Equations and Relationships Fraction Operations Angles and Triangles Geometry and Measurement Relationships

Probability

Notes

Goals

Co

mpletion CertificateCopyright © 2017 by Nelson Education Ltd� Study Planner 151

GREATJOB!

Co

mpletion Certificate

Presented to:

Date:

150 Completion Certificate Copyright © 2017 by Nelson Education Ltd�

9780176823405_M_WB_G8_P3.indd 151 10/01/17 2:22 PM

Copyright © 2006 by Nelson Education Ltd. Chapter 1: Number Relationships 1

1. List all prime numbers between 1 and 20.

2. 1 000 000 is not a prime number. How can you tellthis by looking at it?

3. Identify each number as prime or composite. If thenumber is composite, list all of its factors.

a) 21 d) 39

b) 29 e) 51

c) 33 f) 67

4. A park has the dimensions 17 m by 11 m.

a) Is the area of the park a prime number? ____________

b) How can you tell without calculating the area of the park?

Identifying Prime and CompositeNumbers

Determine whether a number is prime or composite.

At-Home HelpA prime number is a number thathas only two factors: 1 and itself.For example, 17 is a primenumber because its only factorsare 1 and 17.

A composite number is a numberthat has more than two factors.For example, 12 is a compositenumber because its factors are 1,2, 3, 4, 6, and 12.

Use these divisibility rules to helpyou find the factors of a number.

• Numbers ending in 0 or 5 aredivisible by 5.

• Numbers ending in 0 aredivisible by 10.

• Even numbers are divisible by 2.

• If the sum of the digits in anumber is divisible by 3, thenthe number itself is divisibleby 3.

01-Math8WB-CH01 7/27/10 10:01 AM Page 1

Goal

START

FINISH

REWARD CONTRACTWhen you complete a topic in your Nelson Math Workbook, colour in a circle�

My reward will be ���

Name: Date:

Parent/Guardian:

Number Relationships

Proportional Relationships

Collecting, Organizing,

and Displaying Data

Patterns and Relationships

Measurement of Circles

Integer OperationsTransformations

Equations and Relationships

Fraction Operations

Angles and Triangles

Geometry and Measurement Relationships

Probability

iv Reward Contract Copyright © 2017 by Nelson Education Ltd�

9780176823405_M_WB_G8_P3.indd 4 10/01/17 2:20 PM