﻿ Surface Area Worksheets | Problems & Solutions

# Surface Area Worksheets

Surface Area Worksheets
• Page 1
1.
What is the surface area of the sphere in the figure? [Use π = 3.14.]

 a. 1300 cm2 b. 1256 cm2 c. 1500 cm2 d. 1100 cm2

#### Solution:

The radius of the sphere = 10 cm

The surface area of a sphere = 4πr2
[Formula.]

= 4 × 3.14 × 102
[Substitute the values.]

= 12.56 × 100

= 1256 cm2
[Simplify.]

The surface area of the sphere is 1256 cm2.

2.
What is the diameter of the sphere, if the surface area of the sphere is 784$\pi$ ft2?
 a. 30 ft b. 26 ft c. 24 ft d. 28 ft

#### Solution:

The surface area of the sphere = 784π ft2

Let r be the radius of the sphere.

The surface area of the sphere = 4πr2
[Formula.]

784π = 4πr2

784π / = 4πr2/4π
[Divide each side by 4π.]

196 = r2
[Simplify.]

√196 = √(r2)
[Taking square root on both sides.]

14 = r
[Simplify.]

Radius of the sphere = 14 ft

Diameter of the sphere = 2 x radius = 2 x 14 = 28 ft

The diameter of the sphere is 28 ft

3.
What is the surface area of a ball of radius 10 cm?
 a. 1246 cm2 b. 1266 cm2 c. 1256 cm2 d. 1253 cm2

#### Solution:

Surface area of the ball = 4πr2
[Formula.]

= 4 × 3.14 × 100
[Substitute r = 10.]

= 1256 cm2
[Simplify.]

The surface area of the ball is 1256 cm2.

4.
The volume of a sphere is divided by its surface area and the result is 24 cm. What is the radius of the sphere?
 a. 70 cm b. 74 cm c. 72 cm d. 76 cm

#### Solution:

Volume of sphere = 4 / 3 πr3
[Formula.]

Surface area of sphere = 4πr2
[Formula.]

Volume of a sphere ÷ Surface area of the sphere = 24 cm

4 / 3 πr3 ÷ 4πr2 = 24 cm
[Substitute the formulae in step-3.]

r3 = 24
[Simplify.]

r3 x 3 = 24 x 3
[Multiply each side by 3.]

r = 72 cm
[Simplify.]

The radius of the sphere is 72 cm.

5.
What is the ratio of the surface area of a sphere with radius 1 in. to the surface area of a sphere with radius 2 in.?
 a. 3 : 2 b. 1 : 5 c. 1 : 4 d. None of the above

#### Solution:

Radii of two spheres = 1 in. and 2 in.

Surface area of sphere = 4πr2
[Formula.]

Surface area of sphere with radius 1 in. = 4 x π x 12 = 4π x 1 in.2
[Substitute the values and simplify.]

Surface area of sphere with radius 2 in. = 4π x 22 = 4π x 4 in.2
[Substitute the values and simplify.]

Ratio of the surface area of smaller sphere to the bigger sphere = 1 : 4

= 1 : 4
[Simplify.]

The ratio of the surface area of smaller sphere to the bigger sphere is 1 : 4.

6.
What is the surface area of a sphere, if the radius of the sphere is 7 in.? [Use $\pi$ = 3.14.]
 a. 610.44 in.2 b. 620.44 in.2 c. 605.44 in.2 d. 615.44 in.2

#### Solution:

The radius of the sphere, r = 7 in.

The surface area of a sphere = 4πr2
[Formula.]

= 4 × 3.14 × 72
[Substitute the values.]

= 615.44 in.2
[Simplify.]

The surface area of the sphere is 615.44 in.2

7.
What is the surface area of a sphere, if the diameter of the sphere is 8 cm?
 a. 195.96 cm2 b. 200.96 cm2 c. 190.96 cm2 d. 205.96 cm2

#### Solution:

The diameter of the sphere = 8 cm

The radius of the sphere, r = diameter / 2 = 8 / 2 = 4 cm
[Substitute diameter = 8.]

Surface area of a sphere = 4πr2
[Formula.]

= 4 × 3.14 × 42
[Substitute the values.]

= 200.96 cm2
[Simplify.]

The surface area of the sphere is 200.96 cm2.

8.
The surface area of the sphere is 900$\pi$ cm2. Find the radius of the sphere.
 a. 15 cm b. 19 cm c. 13 cm d. 17 cm

#### Solution:

The surface area of the sphere = 900π cm2

Let r be the radius of the sphere.

The surface area of the sphere = 4πr2
[Formula.]

900π = 4πr2

900π/4π = 4πr2/4π
[Divide each side by 4π.]

225 = r2
[Simplify.]

√225 = √r2
[Take square root on both sides.]

15 = r
[Simplify.]

The radius of the sphere is 15 cm.

9.
The diameter of the cone is equal to the diameter of the sphere in the figure. What is the surface area of the sphere?

 a. 90$\pi$ ft2 b. 70$\pi$ ft2 c. 80$\pi$ ft2 d. 64$\pi$ ft2

#### Solution:

The diameter of the cone = 8 ft

The diameter of the cone is equal to the diameter of the sphere.

The diameter of the sphere = 8 ft

The radius of the sphere = diameter / 2 = 8 / 2 = 4 ft
[Substitute diameter = 8.]

Surface area of a sphere = 4πr2
[Formula.]

= 4 x π x 42

= 64π ft2
[Simplify.]

The surface area of the sphere is 64π ft2.

10.
The radius of the cylinder is equal to the radius of the sphere in the figure. What is the ratio of the surface area of the sphere to the surface area of the cylinder?

 a. 2 : 5 b. 1 : 2 c. 1 : 4 d. 1 : 3

#### Solution:

Radius of the sphere = radius of the cylinder = 7 m

Surface area of the sphere = 4πr2
[Formula.]

= 4 x π x 72
[Substitute r = 7.]

= 196π m2
[Simplify.]

Surface area of the cylinder = 2πr2 + 2πrh
[Formula.]

= 2π x 72 + 2π x 7 x 21
[Substitute r = 7.]

= 98π + 294π
[Simplify.]

= 392π m2

= 196π : 392π
Ratio of the surface area of the sphere to the surface area of the cylinder

= 1 : 2
[Simplify.]

The ratio of the surface area of the sphere to the surface area of the cylinder is 1 : 2.