1. Find the surface area of a sphere
EXAMPLE 1
Find the surface area of a sphere
Find the surface area of the sphere.
SOLUTION
S = 4πr2
Formula for surface area of a sphere.
= 4π(82)
Substitute 8 for r.
= 256π
Simplify. ≈
Use a calculator.
The surface area of the sphere is about square
inches.
ANSWER

2. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice
SOLUTION
S = 4πr2
Formula for surface area of a sphere.
20.25π = 4πr2
Substitute 20.25π for S.
= r2
Divide each side by 4π.
2.25 = r
Find the positive square root.

3. EXAMPLE 2
Standardized Test Practice
The diameter of the sphere is 2r = = 4.5
centimeters.
The correct answer is B.
ANSWER

4. GUIDED PRACTICE
for Examples 1 and 2
2. The surface area of a sphere is 30π square meters.
Find the radius of the sphere.
about 2.74 meters
ANSWER

5. EXAMPLE 3
Use the circumference of a sphere
EXTREME SPORTS
In a sport called sphereing, a person rolls down a hill inside an inflatable ball surrounded by another ball. The circumference of the outer ball is 12π feet. Find the surface area of the outer ball.
SOLUTION
The circumference of the outer sphere is 12π feet, so the
radius is = 6 feet.
12π 2π

6. EXAMPLE 3
Use the circumference of a sphere
Use the formula for the surface area of a sphere.
S = 4πr2
= 4π(62)
= 144π
The surface area of the outer ball is 144π, or about
square feet.
ANSWER

7. Find the volume of a sphere
EXAMPLE 4
Find the volume of a sphere
A soccer ball has a diameter of 9 inches. Find its volume.
SOLUTION
The diameter of the ball is 9 inches, so the radius is
= 4.5 inches. 9 2
V = πr3 4 3
Formula for volume of a sphere
= π(4.5)3 4 3
Substitute.

8. Find the volume of a sphere
EXAMPLE 4
Find the volume of a sphere
= 121.5π
Simplify. ≈
Use a calculator.
The volume of the soccer ball is 121.5π, or about
cubic inches.
ANSWER

9. Find the volume of a composite solid
EXAMPLE 5
Find the volume of a composite solid
Find the volume of the composite solid.
SOLUTION
= πr2h – ( πr3) 1 2 4 3
Formulas for volume
= π(2)2(2) – π(2)3 2 3
Substitute. 2 3
= 8π – (8π)
Multiply.

10. Find the volume of a composite solid
EXAMPLE 5
Find the volume of a composite solid
= π – π 24 3 16
Rewrite fractions using least
common denominator. 8 3
= π
Simplify.
The volume of the solid is π, or about 8.38 cubic inches. 8 3
ANSWER