﻿ Surface Area and Volume Worksheet - Page 3 | Problems & Solutions

# Surface Area and Volume Worksheet - Page 3

Surface Area and Volume Worksheet
• Page 3
21.
The base area of a rectangular prism is 4 in.2 and its volume 12 in.3 What is the height of the rectangular prism?
 a. 4 in. b. 2 in. c. 3 in. d. 5 in.

#### Solution:

Volume of a rectangular prism = (Area of the base × height)

12 = 4 × height
[Substitute the values.]

12 / 4 = 3 = height
[Divide each side by 4.]

Height of the rectangular prism = 3 in.

22.
The volume of the box is 150 in.3 and its height is 5 in. Find the area of the base.
 a. 40 in.2 b. 25 in.2 c. 35 in.2 d. 30 in.2

#### Solution:

Volume of the box = (Area of the base × height) unit3

150 = Area of the base × 5
[Substitute the values.]

150 / 5 = Area of the base
[Divide each side by 5.]

Area of the base = 30 in.2

23.
How many cubes are there in the solid?

 a. 14 b. 16 c. 12 d. 10

#### Solution:

Number of cubes in the bottom layer = 4 × 2 = 8

Number of cubes in the top layer = 2 × 2 = 4

Total number of cubes = 8 + 4 = 12

24.
How many small cubes are there in the solid?

 a. 29 b. 30 c. 27 d. 25

#### Solution:

Number of cubes in each layer = 9
[Count the number of cubes in the top layer.]

Number of layers = 3

Total number of cubes = 9 × 3 = 27

25.
How many small cubes are there in the solid?

 a. 24 b. 6 c. 18 d. 12

#### Solution:

Number of cubes in each layer = 6

Number of layers = 2

Total number of cubes = 6 × 2 = 12

26.
Find the volume of a box, which is in the form of a rectangular prism, with a length of 4 m, a height of 6 m and a width of 10 m.
 a. 64 m3 b. 240 m3 c. 24 m3 d. 60 m3

#### Solution:

Volume of a rectangular prism = length × height × width
[Formula.]

Volume of the box = 4 × 6 × 10
[Substitute the values.]

= 240
[Multiply.]

So, the volume of the box is 240 m3.

27.
Find the volume of a cube whose sides measure 8 in.
 a. 8 in3 b. 16 in3 c. 512 in3 d. 64 in3

#### Solution:

The length, width and height of a cube are equal.

Volume of a cube with side a = a × a × a
[Formula.]

= 8 × 8 × 8 = 512
[Substitute and simplify.]

So, the volume of the cube is 512 in3.

28.
What is the surface area of a book 10 cm long, 5 cm wide, and 2 cm high?
 a. 120 cm2 b. 160 cm2 c. 80 cm2 d. 60 cm2

#### Solution:

Length of the book is 10 cm, width is 5 cm and height is 2 cm.

Surface area of the book = 2 (l × w) + 2 (w × h) + 2 (l × h)
[Formula.]

= 2(10 × 5) + 2 (5 × 2) + 2 (10 × 2)
[Substitute the values.]

= 2(50) + 2(10) + 2(20)
[Multiply.]

= 160
[Simplify.]

So, the surface area of the book is 160 cm2.