Math: Volume and Surface Area Worksheet

Question 1

A cube has side length 4 cm. What is its volume?

Accepted Answer

The volume is 64 cubic centimeters because 4 x 4 x 4 = 64.

Question 2

A rectangular prism has length 8 m, width 3 m, and height 5 m. What is its volume?

Accepted Answer

The volume is 120 cubic meters because 8 x 3 x 5 = 120.

Question 3

A cube has side length 6 in. What is its surface area?

Accepted Answer

The surface area is 216 square inches because a cube has 6 equal faces and 6 x 6^2 = 6 x 36 = 216.

Question 4

A rectangular prism has length 7 cm, width 2 cm, and height 4 cm. What is its surface area?

Accepted Answer

The surface area is 100 square centimeters because 2(7 x 2 + 7 x 4 + 2 x 4) = 2(14 + 28 + 8) = 100.

Question 5

A fish tank is shaped like a rectangular prism with dimensions 10 in by 6 in by 8 in. How much water can it hold if filled to the top?

Accepted Answer

The tank can hold 480 cubic inches of water because 10 x 6 x 8 = 480.

Question 6

A gift box measures 9 cm by 5 cm by 3 cm. How much cardboard is needed to cover the outside of the box completely?

Accepted Answer

The box needs 174 square centimeters of cardboard because 2(9 x 5 + 9 x 3 + 5 x 3) = 2(45 + 27 + 15) = 174.

Question 7

A storage bin has a base area of 24 square feet and a height of 5 feet. What is its volume?

Accepted Answer

The volume is 120 cubic feet because volume equals base area times height, so 24 x 5 = 120.

Question 8

A rectangular prism has volume 96 cubic centimeters, length 8 cm, and width 3 cm. What is its height?

Accepted Answer

The height is 4 centimeters because 96 = 8 x 3 x h, so 96 = 24h and h = 4.

Question 9

A cube has a volume of 125 cubic meters. What is the side length of the cube?

Accepted Answer

The side length is 5 meters because 5 x 5 x 5 = 125.

Question 10

Find the surface area of a rectangular prism with length 12 ft, width 4 ft, and height 2 ft.

Accepted Answer

The surface area is 160 square feet because 2(12 x 4 + 12 x 2 + 4 x 2) = 2(48 + 24 + 8) = 160.

Question 11

A cereal box is 10 in tall, 3 in wide, and 2 in deep. Find both its volume and surface area.

Accepted Answer

The volume is 60 cubic inches because 10 x 3 x 2 = 60. The surface area is 112 square inches because 2(10 x 3 + 10 x 2 + 3 x 2) = 2(30 + 20 + 6) = 112.

Question 12

A cube-shaped container has side length 9 cm. How many square centimeters of material are needed to make the container if it is closed on all sides?

Accepted Answer

It needs 486 square centimeters of material because the surface area of a cube is 6s^2, and 6 x 9^2 = 6 x 81 = 486.

Question 13

A rectangular prism has dimensions 5 yd by 4 yd by 3 yd. If the height is doubled, what is the new volume?

Accepted Answer

The new volume is 120 cubic yards because the new height is 6 yards, and 5 x 4 x 6 = 120.

Question 14

A prism has a base area of 18 square inches and a height of 7 inches. What is its volume?

Accepted Answer

The volume is 126 cubic inches because 18 x 7 = 126.

Question 15

A rectangular prism has surface area 94 square centimeters, length 5 cm, width 4 cm, and height h. Find h.

Accepted Answer

The height is 3 centimeters because 94 = 2(5 x 4 + 5h + 4h). This gives 94 = 2(20 + 9h), so 94 = 40 + 18h, then 54 = 18h, and h = 3.

Math: Volume and Surface Area

Math: Volume and Surface Area

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