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1. Find the surface area of the cone.
Round to the nearest tenth.
2. Find the surface area of a cone
with a radius of 6 feet and a
slant height of 10 feet. Round to
the nearest tenth.
3. Find the slant height of a cone with a radius of 4 centimeters and a surface area of 48 square centimeters.
• great circle
• hemisphere
• Recognize and define basic properties of spheres.
• Find surface areas of spheres.
Spheres and Circles
In the figure, O is the center of the sphere, and plane P intersects the sphere in circle R. If OR = 6 centimeters and OS = 14 centimeters, find RS.
Spheres and Circles
Answer: RS is approximately 12.6 centimeters.
The radius of circle R is segment and S is a point on circle R and on sphere O. Use the Pythagorean Theorem for right triangle ORS to solve for RS.
Simplify.
Pythagorean Theorem
Subtract 36 from each side.
Use a calculator.
A. A
B. B
C. C
D. D
A. 7.4 in.
B. 8.5 in.
C. 11 in.
D. 8.7 in.
In the figure, O is the center of the sphere, and plane U intersects the sphere in circle L. If OL = 3 inches and LM = 8 inches, find OM to the nearest tenth.
Surface Area
A. Find the surface area of the sphere, given a great circle with an area of approximately 907.9 square centimeters.
The surface area of a sphere is four times the area of the great circle.
Answer: The surface area is approximately 3631.6 square centimeters.
Surface area of a sphere
Multiply.
Surface Area
B. Find the surface area of a hemisphere with a radius of 3.8 inches.
A hemisphere is half of a sphere. To find the surface area, find half of the surface area of the sphere and add the area of the great circle.
Answer: The surface area is approximately 136.1 square inches.
Surface area of a hemisphere
Use a calculator.
Substitution
1. A
2. B
3. C
4. D
A. 183.2 cm2
B. 366.4 cm2
C. 287.8 cm2
D. 1151.1 cm2
A. Find the approximate surface area of the sphere, given a great circle with an area of approximately 91.6 square centimeters.
1. A
2. B
3. C
4. D
A. 128.7 in2
B. 257.4 in2
C. 386.0 in2
D. 514.7 in2
B. Find the approximate surface area of a hemisphere with a radius of 6.4 inches.
Find the surface area of a ball with a circumference of 24 inches to determine approximately how much leather is needed to make the ball.
Circumference of a circle
First, find the radius of the sphere.
C = 24
Use a calculator.
Divide each side by
Answer: The surface area is approximately 183.3 square inches.
Next, find the surface area of the sphere. Be sure to round to the nearest tenth.
Surface area of a sphere
Use a calculator.
1. A
2. B
3. C
4. D
A. 51.6 in2
B. 254.5 in2
C. 412.5 in2
D. 103.1 in2
Find the surface area of a ball with a circumference of 18 inches to determine how much leather is needed to make the ball.
