warm-up exercises 1. radius 17 m 2. diameter 7.8 in. answer 907.92 m 2 answer 47.78 in. 2 find the...

Warm-Up Exercises

1. Radius 17 m

2. Diameter 7.8 in.

ANSWER 907.92 m2

ANSWER 47.78 in.2

Find the area of each circle.

Warm-Up Exercises

3. Cylinder, radius 6 ft, height 10 ft

ANSWER 1130.97 ft3

Find the volume of each solid.

ANSWER 118.75 cm3

4. Cone, radius 3.1 cm and height 11.8 cm

Warm-Up Exercises

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

ANSWER 301.59 m

Warm-Up ExercisesEXAMPLE 1 Find the surface area of a sphere

SOLUTION

S = 4πr2

= 4π(82)

= 256π

≈ 804.25

Formula for surface area of a sphere.

Substitute 8 for r.

Simplify.

Use a calculator.

Find the surface area of the sphere.

The surface area of the sphere is about 804.25 squareinches.

ANSWER

Warm-Up ExercisesEXAMPLE 2 Standardized Test Practice

SOLUTION

S = 4πr2

20.25π = 4πr2

5.0625 = r2

2.25 = r

Formula for surface area of a sphere.

Substitute 20.25π for S.

Divide each side by 4π.

Find the positive square root.

Warm-Up ExercisesEXAMPLE 2

The diameter of the sphere is 2r = 2 2.25 = 4.5

centimeters.

Standardized Test Practice

The correct answer is B.

ANSWER

Warm-Up ExercisesGUIDED 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 5028.56 feet2

ANSWER

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesEXAMPLE 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 theradius is = 6 feet.12π

2π

Warm-Up ExercisesEXAMPLE 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 452.39 square feet.

ANSWER

Warm-Up ExercisesGUIDED 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.

113.10 ft2ANSWER

Warm-Up ExercisesEXAMPLE 4 Find the volume of a sphere

SOLUTION

The soccer ball has a diameter of 9 inches. Find its volume.

Formula for volume of a sphere

Substitute.

V = πr343

= π(4.5)343

The diameter of the ball is 9 inches, so the radius is

= 4.5 inches.

92

Warm-Up ExercisesEXAMPLE 4 Find the volume of a sphere

= 121.5π

≈ 381.70

Simplify.

Use a calculator.

The volume of the soccer ball is 121.5π, or about 381.70 cubic inches.

ANSWER

Warm-Up ExercisesEXAMPLE 5 Find the volume of a composite solid

SOLUTION

= πr2h – ( πr3)12

43

= π(2)2(2) – π(2)323

Substitute.

Formulas for volume

23

= 8π – (8π) Multiply.

Find the volume of the composite solid.

Warm-Up ExercisesEXAMPLE 5 Find the volume of a composite solid

= π – π243

163

83= π

Rewrite fractions using leastcommon denominator.

Simplify.

The volume of the solid is π, or about 8.38 cubic inches.

83

ANSWER

Warm-Up ExercisesGUIDED PRACTICE for Examples 4 and 5

4. The radius of a sphere is 5 yards. Find the volumeof the sphere. Round your answer to two decimal places.

The volume of the sphere is 523.81yd2

ANSWER

Warm-Up ExercisesGUIDED 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

Warm-Up ExercisesDaily Homework Quiz

Find the surface area and volume of each sphere.

ANSWER

452.39 ft2; 904.78 ft3

1.

r = 6 ft

Warm-Up ExercisesDaily Homework Quiz

2.

d = 12.4 m

ANSWER

483.05 m2; 998.31 m3

Warm-Up ExercisesDaily Homework Quiz

ANSWER

2144.66 in.3

3. A great circle of sphere has circumference 16л in..Find the volume of the sphere.

Warm-Up ExercisesDaily Homework Quiz

ANSWER

251.33 m2; 335.10 m3

4. Find the radius of a sphere with volume 4445.18 ft3.

ANSWER

10.2 ft

5. Find the surface area and volume of the solid.