p t h Surface Area and Volumemrswhitbeck5thgrade.weebly.com/uploads/1/2/5/7/125734541/... · 2020-03-30 · Volume cm3 Volume cm3 Solid has a greater volume than solid . These solids

Lesson 14.1 Building Solids Using Unit Cubes

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

187

Practice 1 Building Solids Using Unit CubesFind the number of unit cubes used to build each solid. Some of the cubes may be hidden.

1. 2.

unit cubes unit cubes

3. 4.


5. 6.


Surface Area and Volume

Cha

pter

Chapter 14 Surface Area and Volume

© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

188

Find the number of unit cubes used to build each solid. Some of the cubes may be hidden.

7. 8.


9. 10.


11.

unit cubes

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

189Lesson 14.2 Drawing Cubes and Rectangular Prisms

Practice 2 Drawing Cubes and Rectangular PrismsDraw on dot paper.

1. Draw a unit cube.

2. Draw two different views of a rectangular prism made up of 2 unit cubes.

3. Draw two different solids made up of 3 unit cubes each.


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

190

Draw each cube or rectangular prism on the dot paper.

4.

5.

6.

Example

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

191Lesson 14.2 Drawing Cubes and Rectangular Prisms

Draw each cube or rectangular prism on the dot paper.

7.

8.

Draw a cube with edges 4 times as long as the edges of this unit cube.

9.


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

192

Complete the drawing of each cube or rectangular prism.

10. 11.

12. 13.

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

193Lesson 14.3 Prisms and Pyramids

Practice 3 Prisms and PyramidsIdentify the type of prism and the shapes of the faces.

1. This is a prism.

2. Two of its faces are .

3. Three of its faces are .

4. This is a prism.

5. All its faces are .


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

194

Complete the table.

Type of Prism Number of Faces

Number of Edges

Number of Vertices

6.

7.

8.

Identify the type of pyramid and the shape of the faces.

9. This is a pyramid.

10. All its faces are .

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

195Lesson 14.3 Prisms and Pyramids

Identify the type of pyramid and the shapes of the faces.

11. This is a pyramid.

12. One of its faces is a .

13. Four of its faces are .

Complete the table.

Type of Pyramid Number of Faces

Number of Edges

Number of Vertices

14.

15.


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

196

Name the solid formed by each net.

16. 17.

18. 19.

20.

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

197Lesson 14.4 Nets and Surface Area

Practice 4 Nets and Surface AreaFind the surface area of each cube.

1.

5 in.

5 in.

5 in.

2.

12 in.12 in.

12 in.

3.

18 cm

18 cm18 cm

Example

3 cm

3 cm

3 cm

3 × 3 = 96 × 9 = 54Surface area of cube = 54 cm2


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

198

Example

Find the surface area of each rectangular prism.

4.

15 in.12 in.

6 in.

5.

19 m

8 m

12 m

8 in. 4 in.

22 in.

2 × 8 × 4 = 642 × 22 × 4 = 1762 × 22 × 8 = 35264 + 176 + 352 = 592Surface area of rectangular prism = 592 in.2

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

199Lesson 14.4 Nets and Surface Area

Find the surface area of each triangular prism.

6.

24 cm

13 cm

35 cm

5 cm

Solve. Show your work.

7. Jeffrey cuts out the net of a box he wants to make. Find the surface area of the box.

10 in.

15 in.

8 in.8 in.

8 in.

Example

2 × 1 2 × 3 × 4 = 12

4 × 18 = 723 × 18 = 545 × 18 = 9012 + 72 + 54 + 90 = 228Surface area of triangular prism = 228 in.2

3 in.5 in.

4 in.18 in.


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

200


8. This glass fish tank does not have a cover. Find the total area of the glass panels used to make the tank.

24 cm 21 cm

27 cm

9. The tank shown is made of steel. It does not have a cover. Find the area of steel sheet used to make the tank.

28 ft

13 ft

6 ft12

10. A rectangular piece of poster board measures 60 centimeters by 80 centimeters. Linn draws the net of a box on the poster board

and cuts it out. If the box measures 10 centimeters by 16 centimeters by 27 centimeters, what is the area of the poster board left?

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

201Lesson 14.5 Understanding and Measuring Volume

Practice 5 Understanding and Measuring VolumeThese solids are formed by stacking unit cubes in the corner of a box. Find the volume of each solid.

1. 2.

Volume � cubic units Volume � cubic units

3. 4.

Volume � cubic units Volume � cubic units


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

202

These solids are formed by stacking 1-centimeter cubes in the corner of a box. Find the volume of each solid.

5. 6.

Volume � cm3 Volume � cm3

7. 8.


9. 10.


Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

203

These solids are built using 1-centimeter cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks.

11.

A B


Solid has a greater volume than solid .

These solids are built using 1-meter cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks.

12.

C D

Volume � m3 Volume � m3

Solid has a lesser volume than solid .

Lesson 14.5 Understanding and Measuring Volume


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

204

These solids are built using 1-inch cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks.

13.

E F

Length � in. Length � in.

Width � in. Width � in.

Height � in. Height � in.

Volume � in.3 Volume � in.3

Solid has a lesser volume than solid .

These solids are built using 1-foot cubes. Find the volume of each solid. Then compare their volumes and fill in the blanks.

14.

G H

Length � ft Length � ft

Width � ft Width � ft

Height � ft Height � ft

Volume � ft3 Volume � ft3

Solid has a greater volume than solid .

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

205

Practice 6 Volume of a Rectangular Prism and Liquid

Write the length, width, and height of each rectangular prism or cube.

Length � cm

Width � cm

Height � cm

1.

12 ft12 ft

20 ft

Length � ft

Width � ft

Height � ft

2.

16 in.

25 in.

12 in.

Length � in.

Width � in.

Height � in.

3.

18 m

18 m

18 m

Length � m

Width � m

Height � m

5 cm8 cm

6 cm

Example8

5

6

Lesson 14.6 Volume of a Rectangular Prism and Liquid


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

206

Find the volume of each rectangular prism.

4.

12 cm

5 cm

9 cm

The length of the rectangular prism is centimeters.

The width of the rectangular prism is centimeters.

The height of the rectangular prism is centimeters.

Volume of the rectangular prism � length � width � height

� � �

� cm3

5.

3 in.

4 in.

2 in.

6.

5 yd

8 yd

3 yd

Volume � Volume �

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

207

Find the volume of each rectangular prism or cube.

7.

4 ft

6 ft

5 ft

8.

16 m

16 m

16 m


9.

4 cm

4 cm

24 cm

10.

3 in.

9 in.7 in.


11.

8 in.

8 in.

7 in.

12.

8 m

3 m5 m




© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

208


Length Width Height Volume

13. 5 cm 12 cm 9 cm

14. 10 in. 25 in. 14 in.

15. 7 m 12 m 8 m

16. 24 ft 10 ft 15 ft


17. Find the volume of a cube with edges measuring 9 centimeters.

18. A rectangular prism has a length of 8 feet and a height of 5 feet. Its length is twice its width. Find the volume of the rectangular prism.

19. The base of a rectangular prism is a square whose sides each measure 9 inches. The height of the rectangular prism is 11 inches. Find its volume.

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

209


Example

� 8 cmh

B � 120 cm2

20.

� 56 m2B

� 6 mh

21.

� 16 ft2B

� 9 fth

Volume = area of base x height = 120 x 8 = 960 cm2



© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

210

22.

� 48 in.2B

� 10 in.h

23.

� 57 m2B

� 5 cmh


24. A rectangular box has a height of 15 meters. The area of its base is 210 square meters. Find the volume of the box.

25. Gerald’s rectangular container has a height of 6 feet and a base area of 72 square feet. How much water would it take to fill the container to the brim?

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

211Lesson 14.6 Volume of a Rectangular Prism and Liquid

Practice 7 Volume of a Rectangular Prism and Liquid

Write each measure in milliliters.

1. 690 cm3 � 2. 207 cm3 �

3. 2,000 cm3 � 4. 4,600 cm3 �

Write each measure in cubic centimeters.

Do you know which national park is the oldest in the United States? Match the letters to the answers to find out.

10,050 2,125 420 420 568 5,060 15,000 3,000 568 7,002 2,125

National Park

Write each measure in liters and milliliters.

13. 720 cm3 � 14. 7,000 cm3 �

15. 2,050 cm3 � 16. 1,470 cm3 �

17. 9,801 cm3 � 18. 4,003 cm3 �

19. 10,600 cm3 � 20. 1,075 cm3 �

5. 420 mL � L

7. 3 L � T

9 2 L 125 mL � E

11. 10 L 50 mL � Y

6. 568 mL � O

8. 15 L � S

10. 5 L 60 mL � W

12. 7 L 2 mL � N


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

212

Find the volume of water in each rectangular tank in milliliters.(Hint: 1 cm3 = 1 mL)

21.

6 cm

12 cm4 cm

22.

9 cm

7 cm5 cm


Find the volume of water in each rectangular tank in liters and milliliters.(Hint: 1,000 cm3 = 1 L)

23.

5 cm

25 cm8 cm

24.

6 cm6 cm

28 cm


25.

9 cm9 cm

18 cm

26.

8 cm7 cm

26 cm


Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.



27. How much water is in this tank when it is 13 full?

28. This rectangular tank is filled with water to a height of 4 centimeters. How much more water is needed to fill the tank completely?

4 cm

18 cm

12 cm

6 cm

12 cm

9 cm

6 cm


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

214


29. A cubical tank with an edge length of 20 centimeters is filled with 3.75 liters of water. How much more water is needed to fill the tank completely? Give your answer in liters.

30. The rectangular tank shown is 14-filled with water. Then another

1 liter 400 milliliters of water is added. Find the volume of water in the tank in the end. Give your answer in liters and milliliters.

20 cm

20 cm

20 cm

8 cm

28 cm

20 cm

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.



31. This container is half-filled with oil. What is the volume of oil in the container? Give your answer in liters and milliliters.

32. A cubical tank whose edges each measure 12 centimeters is half-filled with water. The water is poured into an empty rectangular tank measuring 10 centimeters by 8 centimeters by 7 centimeters until it is full. How much water is left in the cubical tank? Give your answer in milliliters.

19 cm

14 cm14 cm

12 cm

12 cm12 cm

10 cm 8 cm

7 cm


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

216


33. The rectangular swimming pool shown contains 600 cubic meters of water. How much more water has to be added so that the water level is 1 meter from the top?

34. The rectangular tank shown is filled completely with water. How much water must be taken out so the height of the water level in the tank is 10 centimeters? Give your answer in milliliters.

50 m

30 m

3 m

8 cm

15 cm

6 cm

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.



35. The large rectangular tank shown is 45-filled with water.

The water is then poured into the smaller rectangular container until it is full. How much water is left in the tank? Give your answer in liters and milliliters.

12 cm

15 cm15 cm

6 cm5 cm

8 cm


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

218

36. Water flows into this tank at 8 liters per minute. How long will it take to fill the tank?

20 cm

50 cm

60 cm

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

219 Lesson 14.7 Volume of Composite Solids

Practice 8 Volume of Composite SolidsFind the volume of each solid figure.

Example

6 cm

5 cm6 cm

B

A

4 cm

2 cm

1.

10 ftA

B

5 ft

1 ft

5 ft9 ft

Volume of prism A 5

Volume of prism B 5

Volume of the solid 5 1

5 ft3

Volume of prism A = 6 × 5 × 4 = 120 cm3

Volume of prism B = 6 × 4 × 2 = 48 cm3

Volume of the solid = 120 + 48 = 168 cm3

© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

220 Chapter 14 Surface Area and Volume

2.

30 m

A

B

10 m

5 m

15 m

15 m

Volume of prism A 5

Volume of prism B 5

Volume of the solid 5 1

5 m3


3.

10 in.

9 in.8 in.

12 in.

5 in.

Volume 5

4.

6 cm

4 cm

16 cm 10 cm

5 cm

Volume 5

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

221 Lesson 14.7 Volume of Composite Solids

5. A rectangular block of wood is cut into two pieces, as shown below. What is the total volume of the block of wood?

8 ft

2 ft

5 ft

5 ft

© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.



6. A shelf is made up of two rectangular pieces of metal. What is the total volume of metal in the shelf?

30 cm

25 cm

5 cm

8 cm

4 cm

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.


This rectangular container is 25-filled with water.

How much more water is needed to increase the height of the water level to 3 centimeters?

Show two methods of solving this problem.Which method do you prefer? Why?

8 cm

10 cm 5 cm

Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

225

Put On Your Thinking Cap!

Find the number of cubes in each prism.

1. 2.

cubes cubes

Each solid is cut vertically along the line shown. Draw an additional line to complete the two shapes. Then, identify the solid shapes that result.

3.

4.

Challenging Practice


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.

226

5. A rectangular tank is half-filled with water. Another 650 cubic centimeters of water are needed to make it 3

5 full. How much water will be in the

tank when it is 35 full?

6. A cube has a surface area of 216 square centimeters. A second cube has edges that are 3 times as long. How much greater is the

surface area of the second cube than the first cube?


Name: Date: ©

Mar

shal

l Cav

endi

sh In

tern

atio

nal (

Sing

apor

e) P

riva

te L

imite

d.

227

Put On Your Thinking Cap!

Which of these are nets of a cube? Check the boxes.

1. 2.

3. 4.

5. 6.

7. 8.

Problem Solving You may trace, cut out, and fold the nets.


© M

arsh

all C

aven

dish

Inte

rnat

iona

l (Si

ngap

ore)

Pri

vate

Lim

ited.


9. A prism has a square base whose edges each measure 5 centimeters. The ratio of its height to its width is 4 : 1. Find the volume of the rectangular prism in cubic centimeters.

height

5 cm

Documents

p t h Surface Area and Volumemrswhitbeck5thgrade.weebly.com/uploads/1/2/5/7/125734541/... · 2020-03-30 · Volume cm3 Volume cm3 Solid has a greater volume than solid . These solids