Surface Area Worksheets

**Page 1**

1.

What is the surface area of the sphere in the figure? [Use π = 3.14.]

a. | 1300 cm ^{2} | ||

b. | 1256 cm ^{2} | ||

c. | 1500 cm ^{2} | ||

d. | 1100 cm ^{2} |

The surface area of a sphere = 4

[Formula.]

= 4 × 3.14 × 10

[Substitute the values.]

= 12.56 × 100

= 1256 cm

[Simplify.]

The surface area of the sphere is 1256 cm

Correct answer : (2)

2.

What is the diameter of the sphere, if the surface area of the sphere is 784$\pi $ ft^{2}?

a. | 30 ft | ||

b. | 26 ft | ||

c. | 24 ft | ||

d. | 28 ft |

Let

The surface area of the sphere = 4

[Formula.]

784

[Divide each side by 4

196 =

[Simplify.]

√196 = √(

[Taking square root on both sides.]

14 =

[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

Correct answer : (4)

3.

What is the surface area of a ball of radius 10 cm?

a. | 1246 cm ^{2} | ||

b. | 1266 cm ^{2} | ||

c. | 1256 cm ^{2} | ||

d. | 1253 cm ^{2} |

[Formula.]

= 4 × 3.14 × 100

[Substitute

= 1256 cm

[Simplify.]

The surface area of the ball is 1256 cm

Correct answer : (3)

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 |

[Formula.]

Surface area of sphere = 4

[Formula.]

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

[Substitute the formulae in step-3.]

[Simplify.]

[Multiply each side by 3.]

[Simplify.]

The radius of the sphere is 72 cm.

Correct answer : (3)

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 |

Surface area of sphere = 4

[Formula.]

Surface area of sphere with radius 1 in. = 4 x

[Substitute the values and simplify.]

Surface area of sphere with radius 2 in. = 4

[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.

Correct answer : (3)

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} |

The surface area of a sphere = 4

[Formula.]

= 4 × 3.14 × 7

[Substitute the values.]

= 615.44 in.

[Simplify.]

The surface area of the sphere is 615.44 in.

Correct answer : (4)

7.

What is the surface area of a sphere, if the diameter of the sphere is 8 cm?

a. | 195.96 cm ^{2} | ||

b. | 200.96 cm ^{2} | ||

c. | 190.96 cm ^{2} | ||

d. | 205.96 cm ^{2} |

The radius of the sphere,

[Substitute diameter = 8.]

Surface area of a sphere = 4

[Formula.]

= 4 × 3.14 × 4

[Substitute the values.]

= 200.96 cm

[Simplify.]

The surface area of the sphere is 200.96 cm

Correct answer : (2)

8.

The surface area of the sphere is 900$\pi $ cm^{2}. Find the radius of the sphere.

a. | 15 cm | ||

b. | 19 cm | ||

c. | 13 cm | ||

d. | 17 cm |

Let

The surface area of the sphere = 4

[Formula.]

900

900

[Divide each side by 4

225 =

[Simplify.]

√225 = √

[Take square root on both sides.]

15 =

[Simplify.]

The radius of the sphere is 15 cm.

Correct answer : (1)

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 $ ft ^{2} | ||

b. | 70$\pi $ ft ^{2} | ||

c. | 80$\pi $ ft ^{2} | ||

d. | 64$\pi $ ft ^{2} |

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 =

[Substitute diameter = 8.]

Surface area of a sphere = 4

[Formula.]

= 4 x

[Substitute radius = 4.]

= 64

[Simplify.]

The surface area of the sphere is 64

Correct answer : (4)

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 |

Surface area of the sphere = 4π

[Formula.]

= 4 x

[Substitute

= 196

[Simplify.]

Surface area of the cylinder = 2

[Formula.]

= 2

[Substitute

= 98

[Simplify.]

= 392

[Add.]

= 196

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.

Correct answer : (2)

More Surface Area Worksheets | |

Surface Area of Prisms and Cylinders Worksheet | Surface Area of Pyramids and Cones Worksheet |