1. Find the area of each circle.
1. Radius 17 m
ANSWER m2
2. Diameter 7.8 in.
ANSWER
47.78 in.2

2. Find the volume of each solid.
3. Cylinder, radius 6 ft, height 10 ft
ANSWER
ft3
4. Cone, radius 3.1 cm and height 11.8 cm
ANSWER
cm3

3. 5. Find the circumference of a circle with radius 48 m.
ANSWER m

4. 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

5. 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.

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

7. GUIDED PRACTICE
for Examples 1 and 2
1. The diameter of a sphere is 40 feet. Find the
surface area of the sphere.
The surface area of the sphere is about feet2
ANSWER

8. GUIDED PRACTICE
for Examples 1 and 2
2. The surface area of a sphere is 30π square meters.
Find the radius of the sphere.
2.71
ANSWER

9. 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

10. 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

11. GUIDED PRACTICE
for Example 3
3. In Example 3, the circumference of the inner ball is 6π feet. Find the surface area of the inner ball. round your answer to two decimal places.
ft2
ANSWER

12. Find the volume of a sphere
EXAMPLE 4
Find the volume of a sphere
The 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.

13. 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

14. 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.

15. 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

16. GUIDED PRACTICE
for Examples 4 and 5
4. The radius of a sphere is 5 yards. Find the volume
of the sphere. Round your answer to two decimal
places.
The volume of the sphere is yd2
ANSWER

17. GUIDED PRACTICE
for Examples 4 and 5
5. A solid consists of a hemisphere of radius 1 meter on top of a cone with the same radius and height 5 meters. Find the volume of the solid. Round your answer to two decimal places.
The volume of the solid is 7.33m2
ANSWER

18. Daily Homework Quiz
Find the surface area and volume of each sphere. 1.
r = 6 ft
ANSWER
ft2; ft3

19. Daily Homework Quiz 2.
d = 12.4 m
ANSWER
m2; m3

20. Daily Homework Quiz
3. A great circle of sphere has circumference 16л in..
Find the volume of the sphere.
ANSWER
in.3

21. Daily Homework Quiz
4. Find the radius of a sphere with volume
ft3.
ANSWER
10.2 ft
5. Find the surface area and volume of the solid.
ANSWER
m2; m3