Surface Areas and Volumes of Spheres LESSON 11-6 Additional Examples

Find the surface area of the sphere below. Leave your answer in terms of .

S.A. = 4

r

2 Use the formula for the surface area of a sphere.

= 4 = 324 • 9 2 Substitute

r

= 18 2 = 9.

Simplify.

The surface area of the sphere is 324 ft 2 .

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Surface Areas and Volumes of Spheres LESSON 11-6 Additional Examples Quick Check

The circumference of a rubber ball is 13 cm. Approximate its surface area to the nearest whole number.

Step 1:

Use the circumference to find the radius in terms of .

C

= 2

r

Use the formula for circumference.

13 = 2

r

Substitute 13 for

C

.

2 13 =

r

Step 2:

Solve for

r

.

Use the radius to find the surface area.

S.A. = 4

r

2 = 4 = 169 • ( ) 2 2 Use the formula for the surface area of a sphere.

13 Substitute for

r

.

Simplify.

2 Use a calculator.

To the nearest whole number, the surface area of the rubber ball is 54 cm 2 .

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Surface Areas and Volumes of Spheres LESSON 11-6 Additional Examples

Find the volume of the sphere. Leave your answer in terms of .

V

=

r

3 3 Use the formula for the volume of a sphere.

= • 15 3 3 Substitute

r

30 = = 15.

2 = 4500 Simplify.

The volume of the sphere is 4500 cm 3 .

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Surface Areas and Volumes of Spheres LESSON 11-6 Additional Examples

The volume of a sphere is 1 in.

3 . Find its surface area to the nearest tenth.

Step 1:

Use the volume to find the radius

r

.

V

=

r

3 3 1 =

r

3 3 3 4 =

r

3 3 3 4 =

r r

Use the formula for the volume of a sphere.

Substitute.

Solve for

r

3 .

Find the cube root of each side.

Use a calculator.

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Surface Areas and Volumes of Spheres LESSON 11-6 Additional Examples (continued) Step 2:

Use the radius to find the surface area.

S.A. = 4

r

2 4 (0.62035049) 2 Use the formula for the surface area of a sphere.

Substitute.

Use a calculator.

To the nearest tenth, the surface area of the sphere is 4.8 in.

2 .

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