Surface Area & Volume of Spheres

Section 11-6

Vocab• Sphere - the set of all points in space

equidistant from a given point called the center.

• Radius - segment that has one endpoint at the center and the other endpoint on the sphere.

• Diameter - segment passing through the center with endpoints on the sphere.

Surface Area of a Sphere

= 324 Simplify.

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 • 92 Substitute r = = 9.18 2

The surface area of the sphere is 324 ft2.

Your turn• Find the S.A. of a sphere with a

diameter of 14 in. Give your answer two ways, in terms of π and rounded to the nearest square inch.

• 196π in2; 616 in2

S.A. = 4 r 2 Use the formula for the surface area of a sphere.

13 = 2 r Substitute 13 for C. C = 2 r Use the formula for circumference.Step 1: Use the circumference to find the radius in terms of .

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

= r Solve for r.132Step 2: Use the radius to find the surface area.

= 4 • ( )2 Substitute for r.132

132

To the nearest whole number, the surface area of the rubber ball is 54 cm2.

= Simplify.169

53.794371 Use a calculator.

Your turn• Find the S.A. of a melon with a

circumference of 18 in. Round your answer to the nearest ten square inches.

• 100 in2

Volume of a sphere

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

V = r 3 Use the formula for the volume of a sphere.43

302 = • 153 Substitute r = = 15.4

3

= 4500 Simplify.

The volume of the sphere is 4500 cm3.

Your turn• Find the volume to the nearest

cubic inch of a sphere with a diameter of 60 inches.

• 113,097 in3

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 Use the formula for the volume of a sphere.43

1 = r 3 Substitute.43

= r 3 Solve for r 3. 34

= r Find the cube root of each side. 34

3

r 0.62035049 Use a calculator.

Step 2: Use the radius to find the surface area.

S.A. = 4 r 2 Use the formula for the surface area of a sphere.

4 (0.62035049)2 Substitute.

4.8359744 Use a calculator.

To the nearest tenth, the surface area of the sphere is 4.8 in.2.

(continued)

Your Turn• The volume of a sphere is 4200 ft3.

Find S.A. to the nearest tenth.• 1258.9 ft3