11(M)MIF2015CC_RTG5B

Worksheet 1 Building Solids Using Unit Cubes

How many unit cubes are used to build each solid?

This is a unit cube.

1. 2.

unit cubes unit cubes

3. 4.

unit cubes unit cubes

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C

H

A

P

T

E

R

Surface Area and Volume

14

5. 6.

unit cubes unit cubes

7. 8.

unit cubes unit cubes

9. 10.

unit cubes unit cubes

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Chapter 14 Lesson 14.1

Worksheet 2 Drawing Cubes and Rectangular Prisms

Draw these cubes or rectangular prisms on the dot paper without showing

the unit cubes.

Example

1.

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2.

3.

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Chapter 14 Lesson 14.2

4.

Complete the drawing of each cube or rectangular prism.

5.

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6.

Draw a rectangular prism that has edges 3 times as long as this prism.

7.

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Chapter 14 Lesson 14.2

Worksheet 3 Prisms and Pyramids

Complete.

Example

In the ﬁgures, circle two vertices and shade two faces gray.

One of the faces of

the square pyramid

is a square.

1. In the ﬁgures, circle three vertices and color three edges gray.

The triangular pyramid

has 6 edges.

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Circle the shape(s) that can be found in the ﬁgure.

Example

The base of the pentagonal

prism is a pentagon. The other

faces are rectangles.

Triangle Square Rectangle

Parallelogram Pentagon Hexagon

2.

Triangle Square Rectangle

Parallelogram Pentagon Hexagon

Shade each solid shape if it has two identical and parallel faces.

3.

Put a check in the box if the solid ﬁgure is a prism.

4.

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Chapter 14 Lesson 14.3

Match the names to the solid ﬁgures.

5.

Rectangular prism

Pentagonal prism

Triangular prism

Octagonal prism

Hexagonal prism

Complete the table.

Type of Prism

Number of

Faces

Number of

Edges

Number of

Vertices

6. Rectangular

7. Pentagonal

8. Triangular

9. Octagonal

10. Hexagonal

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Put a check in the box if the solid ﬁgure is a pyramid.

Shade the base of each pyramid.

11.

Match the names to the solid ﬁgures.

12.

Triangular pyramid

Rectangular pyramid

Pentagonal pyramid

Hexagonal pyramid

Octagonal pyramid

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Chapter 14 Lesson 14.3

Complete the table.

Type of

Pyramid

Number of

Faces

Number of

Edges

Number of

Vertices

13. Triangular

14. Rectangular

15. Pentagonal

16. Hexagonal

17. Octagonal

These are the nets of some pyramids.

Shade the base of each pyramid.

18.

More than one net may form

the same solid ﬁgure.

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These are the nets of some prisms. Shade the identical and

parallel edges of each prism using different colors.

19.

Match the nets with the solid ﬁgure they form.

20.

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Chapter 14 Lesson 14.3

21. Explain the statements.

a. A cube is a rectangular prism.

b. A cone is not a prism.

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22. For each ﬁgure, identify whether or not it is a prism. Explain your reasoning.

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Chapter 14 Lesson 14.3

Worksheet 4 Nets and Surface Area

Find the surface area of each cube.

4 in.

Example

The surface area is equal

to the sum of the areas of

the 6 square faces.

Area of one square face 5 4 3 4

5 16 in.

2

Surface area of the cube 5 6 3 16

5 96 in.

2

1.

7 cm

2.

14 in.

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Chapter 14 Lesson 14.4

Find the surface area of each rectangular prism.

(7 3 4) (7 3 4)

(7 3 4)

(5 3 4)

40 cm

2

(5 3 4)

(7 3 5)

2

Example

Area of 2 gray rectangles 5 1

5 3

5

Area of 2 white rectangles 5 1

5 3

5

Area of 2 black rectangles 5 1

5 3

5

Surface area of the rectangular prism 5 56 1 70 1 40

5 166 cm

2

56 cm

2

70 cm

2

7 cm

4 cm

5 cm

4 cm

5 cm

7 cm

4 cm

5 cm

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Chapter 14 Lesson 14.4

3.

13 in.

8 in.

6 in.

4.

17 in.

8 in.

5.

9 m

2 m

11 m

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Find the surface area of each triangular prism.

Example

4 cm

8 cm

5 cm

3 cm

8 cm

5 cm

3 cm

3 cm 4 cm 5 cm

Area of triangles 5 3

5 3

5

Area of white rectangle 5 3

5

Area of black rectangle 5

5

Area of gray rectangle 5

5

Surface area of the triangular prism 5 12 1 24 1 32 1 40

5 108 cm

2

6

12 cm

2

8

24 cm

2

40 cm

2

8 3 4

8 3 5

32 cm

2

3

2

1

_

2

3 3 3 4

( )

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Chapter 14 Lesson 14.4

6.

The base of this triangular

prism is a right triangle.

6 cm

8 cm

10 cm

22 cm

7.

5 in.

29 in.

8 in.

3 in.

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Solve. Show your work.

8. A rectangular cupboard measures 110 centimeters by 85 centimeters by

40 centimeters. What is the surface area of the cupboard?

9. A rectangular display cabinet measures 96 centimeters by 78 centimeters

by 34 centimeters. What is the surface area of the outside of the cabinet

if it does not have a cover?

96 cm

78 cm

34 c

m

10. A rectangular bedroom measures 12 feet by 8

1

_

2

feet by 7 feet. The rectangular

door in the bedroom measures 2 feet by 6

1

_

2

feet. Joanne decides to paint the

walls of the room pink. Find the surface area of the walls in the room.

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Chapter 14 Lesson 14.4

Worksheet 5 Understanding and Measuring Volume

These solids are formed by stacking 1-centimeter cubes. Find the volume of

each solid.

1. 2.

Volume 5 cm

3

Volume 5 cm

3

3. 4.

Volume 5 cm

3

Volume 5 cm

3

5. 6.

Volume 5 cm

3

Volume 5 cm

3

7. 8.

Volume 5 cm

3

Volume 5 cm

3

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These solids are built using unit cubes. Find the volume of each solid.

Then compare the volumes and ﬁll in the blanks.

Example

Volume 5 cubic units Volume 5 cubic units

Solid

has a larger volume than solid .

A

B

17

A B

10

These solids are built using 1-inch cubes. Find the volume of each solid.

Then compare their volumes and ﬁll in the blanks.

9.

C

D

Volume 5 in.

3

Volume 5 in.

3

Solid has a lesser volume than solid .

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Chapter 14 Lesson 14.5

These solids are built using 1-foot cubes. Find the volume of each solid.

Then compare their volumes and ﬁll in the blanks.

10.

E

F

Volume 5 ft

3

Volume 5 ft

3

Solid has a larger volume than solid .

These solids are built using 1-centimeter cubes. Find the volume of each

solid. Then compare their volumes and ﬁll in the blanks.

11.

G

H

Length 5 cm Length 5 cm

Width 5

cm Width 5 cm

Height 5

cm Height 5 cm

Volume 5

cm

3

Volume 5 cm

3

Solid has a larger volume than solid .

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These solids are built using 1-meter cubes. Find the volume of each solid.

Then compare their volumes and ﬁll in the blanks.

12.

K

M

Length 5 m Length 5 m

Width 5

m Width 5 m

Height 5

m Height 5 m

Volume 5

m

3

Volume 5 m

3

Solid has a smaller volume than solid .

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Chapter 14 Lesson 14.5

Worksheet 6 Volume of a Rectangular Prism and Liquid

Find the volume of each rectangular prism or cube.

1.

18 c

m

35 cm

27 cm

Volume 5

8 cm

Length 5

cm

Width 5

cm

Height 5

cm

Volume 5 length

3 width 3 height

5 edge

3 edge 3 edge

5

3 3

5

512 cm

3

8

8 8 8

Example

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2.

13 m

Volume 5

3.

15 m

20 m

38 m

Volume 5

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Chapter 14 Lesson 14.6

4.

48 in.

26 in.

19 in.

Volume 5

5.

9 in.

9 in

.

Volume 5

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6.

18 ft

34 ft

21 f

t

Volume 5

7.

15 ft

15 f

t

Volume 5

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Chapter 14 Lesson 14.6

Solve. Show your work.

17 cm

14.5 cm

12 cm

Example

The capacity of a

container is the liquid

volume of the container.

Steven ﬁlls a rectangular container measuring

17 centimeters by 14.5 centimeters by

12 centimeters with orange juice. How many

liters and milliliters of orange juice are in the

container?

Volume of orange juice in the container

5 17 cm 3 14.5 cm 3 12 cm

5 2,958 cm

3

5 2,958 mL

5 2 L 958 mL

Remember that 1 cm

3

5 1 mL.

8. The base of a miniature rectangular ﬁsh tank measures 8 centimeters by

4.5 centimeters. The height of the tank is 6 centimeters. Find the capacity

of the tank in liters and milliliters.

8 cm

4.5 c

m

6 cm

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9. A rectangular container measures 6 centimeters by 3.5 centimeters by

12 centimeters. It is completely ﬁlled with water. How many liters and

milliliters of water are in the container?

6 cm

3.5 cm

12 cm

10. A rectangular box measures 15 centimeters by 9 centimeters by

13 centimeters. Shannon uses the box to mix glue for her project.

She ﬁlls the entire box with glue. How many liters and milliliters

of glue are in the box?

15 cm

9 cm

13 c

m

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Chapter 14 Lesson 14.6

11. A rectangular container is

1

_

2

-ﬁlled with water. How much water is needed

to ﬁll the container? After the container is ﬁlled, how much water must be

poured out so that the container is

1

_

3

full?

12 cm

15 cm

8 cm

12. A tank is

1

_

2

-ﬁlled with water. Some of the water is then poured into 8 small

containers each with a capacity of 27 cubic centimeters. The tank is now

1

_

4

full. What is the capacity of the tank?

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13. A swimming pool, 25 meters wide, 50 meters long, and 12 meters deep,

is

2

_

3

-ﬁlled with water. Its cross section is as shown below. How much water

must be drained off so that the water level falls to 5 meters?

40 m

3 m

9 m

5 m

14. Complete the statements.

a. Volume of a rectangular prism 5 length 3

3

b. Volume of a cube 5 3 width 3

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Chapter 14 Lesson 14.6

15. Label the two rectangular prisms.

Fill in the blanks with length, width and height.

16. In the diagram, the base 5 63 m

2

and height 5 8 m. Find the volume of the

rectangular prism.

8 m

B

 63 m

2

Volume 5 cubic meters.

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17. Find the volume of the prism.

9 yd

4 yd

9 yd

Volume 5

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Chapter 14 Lesson 14.6

Worksheet 7 Volume of Composite Solids

Complete.

A solid is made from two rectangular prisms. Find the volume of the solid.

9 cm

B

A

7 cm

4 cm

6 cm

3 cm

a. Volume of prism A 5 3 3 5 cm

3

b. Volume of prism B 5 3 3 5 cm

3

c. Volume of the solid 5 1 5 cm

3

84

4

6

162 246

7

9

84

162

Example

1. A solid is made from two rectangular prisms.

Find the total volume of the solid.

16 cm

8 cm

12 c

m

A

6 cm

5 cm

B

a. Volume of prism A 5 3 3 5 cm

3

b. Volume of prism B 5 3 3 5 cm

3

c. Volume of the solid 5 1 5 cm

3

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Solve. Show your work.

2. Find the volume of the rectangular prism after a cube is removed from it.

9 cm

4 cm

15 cm

3. Find the volume of the solid which is made up of two prisms.

18 in.12 in.

9 in.

5 in.

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Chapter 14 Lesson 14.7