Warm-Up Exercises 1. Radius 17 m 2. Diameter 7.8 in. ANSWER 907.92 m 2 ANSWER 47.78 in. 2 Find the...
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Transcript of 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.