12-6 Surface Area and Volumes of Spheres
Find the surface area of each sphere or hemisphere. Round to the nearest tenth.
1. SOLUTION: 2. SOLUTION: 2
3. sphere: area of great circle = 36π yd
SOLUTION: We know that the area of a great circle is
. Find r.
Now find the surface area.
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4. hemisphere: circumference of great circle ≈ 26 cm
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12-6 Surface Area and Volumes of Spheres
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3. sphere: area of great circle = 36π yd
SOLUTION: We know that the area of a great circle is
. Find r.
Now find the surface area.
4. hemisphere: circumference of great circle ≈ 26 cm
SOLUTION: We know that the circumference of a great circle is
.
The area of a hemisphere is one-half the area of the sphere plus the area of the great circle.
Find the volume of each sphere or hemisphere. Round to the nearest tenth.
5. sphere: radius = 10 ft
SOLUTION: 6. hemisphere: diameter = 16 cm
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SOLUTION: Page 2
12-6 Surface Area and Volumes of Spheres
6. hemisphere: diameter = 16 cm
SOLUTION: 7. hemisphere: circumference of great circle = 24π m
SOLUTION: We know that the circumference of a great circle is
. Find r.
Now find the volume.
2
8. sphere: area of great circle = 55π in
SOLUTION: We know that the area of a great circle is
. Find r.
Now find the volume.
9. BASKETBALL Basketballs used in professional games must have a circumference of 29
surface area of a basketball used in a professional game?
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SOLUTION: We know that the circumference of a great circle is 2πr . Find r.
inches. What is the
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12-6 Surface Area and Volumes of Spheres
9. BASKETBALL Basketballs used in professional games must have a circumference of 29
inches. What is the
surface area of a basketball used in a professional game?
SOLUTION: We know that the circumference of a great circle is 2πr . Find r.
Find the surface area.
Find the surface area of each sphere or hemisphere. Round to the nearest tenth.
10. SOLUTION: 11. SOLUTION: eSolutions Manual - Powered by Cognero
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12-6 Surface Area and Volumes of Spheres
11. SOLUTION: 12. SOLUTION: 13. SOLUTION: 14. sphere: circumference of great circle = 2π cm
SOLUTION: We know
the circumference
of a great circle is 2πr. Find r.
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12-6 Surface Area and Volumes of Spheres
14. sphere: circumference of great circle = 2π cm
SOLUTION: We know that the circumference of a great circle is 2πr. Find r.
2
15. sphere: area of great circle ≈ 32 ft
SOLUTION: 2
We know that the area of a great circle is πr . Find r.
2
16. hemisphere: area of great circle ≈ 40 in
SOLUTION: 2
We know that the area of a great circle is πr . Find r.
Substitute for r2 in the surface area formula.
17. hemisphere: circumference of great circle = 15π mm
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SOLUTION: Page 6
12-6 Surface Area and Volumes of Spheres
17. hemisphere: circumference of great circle = 15π mm
SOLUTION: CCSS PRECISION Find the volume of each sphere or hemisphere. Round to the nearest tenth.
18. SOLUTION: The volume V of a hemisphere is
or , where r is the radius. The radius is 5 cm.
19. SOLUTION: The volume V of a sphere is
, where r is the radius. The radius is 1 cm.
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20. sphere:
SOLUTION: Page 7
12-6 Surface Area and Volumes of Spheres
20. sphere: radius = 1.4 yd
SOLUTION: The volume V of a sphere is
, where r is the radius.
21. hemisphere: diameter = 21.8 cm
SOLUTION: The radius is 10.9 cm. The volume V of a hemisphere is
or , where r is the radius.
2
22. sphere: area of great circle = 49π m
SOLUTION: The area of a great circle is
.
The volume V of a sphere is
, where r is the radius.
23. sphere: circumference of great circle ≈ 22 in.
SOLUTION: The circumference of a great circle is
The volume V of a sphere is
.
, where r is the radius.
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24. hemisphere: circumference of great circle ≈ 18 ft
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12-6 Surface Area and Volumes of Spheres
23. sphere: circumference of great circle ≈ 22 in.
SOLUTION: The circumference of a great circle is
The volume V of a sphere is
.
, where r is the radius.
24. hemisphere: circumference of great circle ≈ 18 ft
SOLUTION: The circumference of a great circle is
.
The volume V of a hemisphere is
or , where r is the radius.
or , where r is the radius.
2
25. hemisphere: area of great circle ≈ 35 m
SOLUTION: The area of a great circle is
.
The volume V of a hemisphere is
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12-6 Surface Area and Volumes of Spheres
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25. hemisphere: area of great circle ≈ 35 m
SOLUTION: The area of a great circle is
.
The volume V of a hemisphere is
or , where r is the radius.
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