M
Math Coach Amy
Amy Ferguson Moncure

7th Grade Math · Unit 8

Volume or
Surface Area

Decide whether the situation asks for the space inside or the covering on the outside. Then use the formula that matches.

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Key Ideas Easy Medium Hard
What to Remember

Volume

Volume is the space inside.

Filling, pouring, or storing asks for volume.

Surface area

Surface area is the outside.

Painting, wrapping, or covering the outside asks for surface area.

Do not swap them

A label, a wrap, or a coat of paint is not a volume.

Water, soup, sand, or storage inside a container is not a surface area.

Level 1

Easy

Decide the measure. Do not compute yet.

Example
A tank is filled with water. Are you finding volume or surface area?

The water fills the space inside the tank.

Answer: Volume

1
A can is filled with soup. Are you finding volume or surface area?
Show Answer

The soup fills the space inside the can.

Answer: Volume

2
Sand is poured into a box until the box is full. Are you finding volume or surface area?
Show Answer

The sand fills the space inside the box.

Answer: Volume

3
You want the storage space inside a crate. Are you finding volume or surface area?
Show Answer

Storage is the space inside the crate.

Answer: Volume

4
You wrap a box. Are you finding volume or surface area?
Show Answer

Wrapping covers the outside of the box.

Answer: Surface area

5
You paint the outside of a box. Are you finding volume or surface area?
Show Answer

Paint covers the outside.

Answer: Surface area

6
A label covers the outside of a can. Are you finding volume or surface area?
Show Answer

A label covers the outside.

Answer: Surface area

7
Gift paper covers a present. Are you finding volume or surface area?
Show Answer

Gift paper covers the outside.

Answer: Surface area

8
A cylindrical tank is filled with water. Are you finding volume or surface area?
Show Answer

The water fills the space inside the tank.

Answer: Volume

9
You paint the outside of a water tank. Are you finding volume or surface area?
Show Answer

Paint covers the outside of the tank.

Answer: Surface area

10
You want to know how much oatmeal fits inside a canister. Are you finding volume or surface area?
Show Answer

The oatmeal fills the space inside.

Answer: Volume

Level 2

Medium

Decide, then find the measure for the rectangular prism.

Example
Sand fills a rectangular prism that is 2 in by 3 in by 4 in. How much sand is inside?

This asks for volume because it is the space inside.

V = lwh

V = 2 × 3 × 4

V = 24

Answer: 24 cubic in

1
Water fills a rectangular prism that is 2 cm by 5 cm by 6 cm. How much water is inside?
Show Answer

This asks for volume because it is the space inside.

V = lwh

V = 2 × 5 × 6

V = 60

Answer: 60 cubic cm

2
A crate holds storage. The rectangular prism is 4 ft by 5 ft by 2 ft. How much storage is inside?
Show Answer

This asks for volume because it is the space inside.

V = lwh

V = 4 × 5 × 2

V = 40

Answer: 40 cubic ft

3
Soup fills a rectangular carton that is 3 in by 3 in by 4 in. How much soup is inside?
Show Answer

This asks for volume because it is the space inside.

V = lwh

V = 3 × 3 × 4

V = 36

Answer: 36 cubic in

4
Sand fills a rectangular prism that is 5 cm by 2 cm by 3 cm. How much sand fills it?
Show Answer

This asks for volume because it is the space inside.

V = lwh

V = 5 × 2 × 3

V = 30

Answer: 30 cubic cm

5
A bin stores items. The rectangular prism is 6 in by 2 in by 4 in. How much storage is inside the bin?
Show Answer

This asks for volume because it is the space inside.

V = lwh

V = 6 × 2 × 4

V = 48

Answer: 48 cubic in

6
Gift paper covers the outside of a rectangular prism that is 4 in by 4 in by 4 in. How much paper covers the outside?
Show Answer

This asks for surface area because it covers the outside.

SA = 2lw + 2lh + 2wh

SA = 2(4)(4) + 2(4)(4) + 2(4)(4)

SA = 2(16) + 2(16) + 2(16)

SA = 32 + 32 + 32

SA = 96

Answer: 96 square in

7
Paint covers the outside of a rectangular prism that is 6 cm by 3 cm by 2 cm. How much area is painted?
Show Answer

This asks for surface area because it covers the outside.

SA = 2lw + 2lh + 2wh

SA = 2(6)(3) + 2(6)(2) + 2(3)(2)

SA = 2(18) + 2(12) + 2(6)

SA = 36 + 24 + 12

SA = 72

Answer: 72 square cm

8
Wrapping covers the outside of a rectangular prism that is 8 ft by 2 ft by 1 ft. How much wrap covers the outside?
Show Answer

This asks for surface area because it covers the outside.

SA = 2lw + 2lh + 2wh

SA = 2(8)(2) + 2(8)(1) + 2(2)(1)

SA = 2(16) + 2(8) + 2(2)

SA = 32 + 16 + 4

SA = 52

Answer: 52 square ft

9
Gift paper covers the outside of a rectangular prism that is 5 in by 1 in by 2 in. How much paper is used on the outside?
Show Answer

This asks for surface area because it covers the outside.

SA = 2lw + 2lh + 2wh

SA = 2(5)(1) + 2(5)(2) + 2(1)(2)

SA = 2(5) + 2(10) + 2(2)

SA = 10 + 20 + 4

SA = 34

Answer: 34 square in

10
Paint covers the outside of a rectangular prism that is 7 cm by 3 cm by 2 cm. How much area gets painted?
Show Answer

This asks for surface area because it covers the outside.

SA = 2lw + 2lh + 2wh

SA = 2(7)(3) + 2(7)(2) + 2(3)(2)

SA = 2(21) + 2(14) + 2(6)

SA = 42 + 28 + 12

SA = 82

Answer: 82 square cm

Level 3

Hard

Decide, then find the measure for the right cylinder.

Example
Soup fills a right cylinder with radius 3 cm and height 10 cm. How much soup is inside?

This asks for volume because it is the space inside.

V = πr²h

V = π × 3² × 10

3² = 9

V = π × 9 × 10

V = 90π

Answer: 90π cubic cm

1
Water fills a right cylinder with radius 4 ft and height 10 ft. How much water is inside?
Show Answer

This asks for volume because it is the space inside.

V = πr²h

V = π × 4² × 10

4² = 16

V = π × 16 × 10

V = 160π

Answer: 160π cubic ft

2
Soup fills a right cylinder with radius 2 in and height 8 in. How much soup fills the can?
Show Answer

This asks for volume because it is the space inside.

V = πr²h

V = π × 2² × 8

2² = 4

V = π × 4 × 8

V = 32π

Answer: 32π cubic in

3
Paint covers the whole outside of a right cylinder with radius 3 in and height 6 in. The paint includes the top and the bottom. How much area is painted?
Show Answer

This asks for surface area because it covers the outside.

SA = 2πr² + 2πrh

SA = 2π3² + 2π(3)(6)

3² = 9

SA = 18π + 36π

SA = 54π

Answer: 54π square in

4
Sand fills a right cylinder with radius 5 cm and height 6 cm. How much sand is inside?
Show Answer

This asks for volume because it is the space inside.

V = πr²h

V = π × 5² × 6

5² = 25

V = π × 25 × 6

V = 150π

Answer: 150π cubic cm

5
Gift paper covers the whole outside of a right cylinder with radius 2 cm and height 8 cm. The paper includes the top and the bottom. How much paper is used?
Show Answer

This asks for surface area because it covers the outside.

SA = 2πr² + 2πrh

SA = 2π2² + 2π(2)(8)

2² = 4

SA = 8π + 32π

SA = 40π

Answer: 40π square cm

6
A cylindrical crate is a right cylinder with radius 3 ft and height 6 ft. How much storage is inside?
Show Answer

This asks for volume because it is the space inside.

V = πr²h

V = π × 3² × 6

3² = 9

V = π × 9 × 6

V = 54π

Answer: 54π cubic ft

7
Paint covers the whole outside of a right cylinder with radius 5 ft and height 4 ft. The paint includes the top and the bottom. How much of the drum is painted?
Show Answer

This asks for surface area because it covers the outside.

SA = 2πr² + 2πrh

SA = 2π5² + 2π(5)(4)

5² = 25

SA = 50π + 40π

SA = 90π

Answer: 90π square ft

8
Oatmeal fills a right cylinder with radius 4 cm and height 9 cm. How much oatmeal is inside?
Show Answer

This asks for volume because it is the space inside.

V = πr²h

V = π × 4² × 9

4² = 16

V = π × 16 × 9

V = 144π

Answer: 144π cubic cm

9
A cover goes over the entire outside of a right cylinder with radius 4 cm and height 5 cm. The cover includes the top and the bottom. How much material covers it?
Show Answer

This asks for surface area because it covers the outside.

SA = 2πr² + 2πrh

SA = 2π4² + 2π(4)(5)

4² = 16

SA = 32π + 40π

SA = 72π

Answer: 72π square cm

10
Paint covers the whole outside of a right cylinder with radius 6 ft and height 3 ft. The paint includes the top and the bottom. How much of the tank is painted?
Show Answer

This asks for surface area because it covers the outside.

SA = 2πr² + 2πrh

SA = 2π6² + 2π(6)(3)

6² = 36

SA = 72π + 36π

SA = 108π

Answer: 108π square ft

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