12-4 Volume of Pyramids, Cones and Spheres
Find the volume of each figure. Round to the nearest tenth, if necessary.
1. SOLUTION: The radius of the base is half the diameter, so 7 ÷ 2 = 3.5.
The volume of the cone is about 115.5 cubic inches.
2. SOLUTION: The volume of the pyramid is about 245.6 cubic millimeters.
3. SOLUTION: The volume of the pyramid is about 74.2 cubic centimeters.
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12-4 Volume of Pyramids, Cones and Spheres
The volume of the pyramid is about 74.2 cubic centimeters.
4. SOLUTION: The volume of the sphere is about 1436.8 cubic yards.
5. JEWELRY Amber purchased a necklace that contained an 8 millimeter diameter round pearl. Find the volume of
the pearl to the nearest tenth.
SOLUTION: The radius of the pearl is half the diameter, so 8 ÷ 2 = 4.
The volume of the pearl is about 268.1 cubic millimeters.
Find the volume of each figure. Round to the nearest tenth, if necessary.
6. SOLUTION: The volume of the pyramid is 400 cubic millimeters.
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12-4The
Volume
Cones
and Spheres
volume ofofthePyramids,
pyramid is 400
cubic millimeters.
7. SOLUTION: The volume of the cone is about 392.7 cubic feet.
8. SOLUTION: The volume of the cone is about 6.7 cubic feet.
9. (See page 728 of your text.)
SOLUTION: The volume of the square pyramid is 6 cubic feet.
10. (See page 728 of your text.)
SOLUTION: The radius of the sphere is half the diameter, so 12 ÷ 2 = 6.
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The volume of the sphere is about 904.8 cubic inches.
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12-4 Volume of Pyramids, Cones and Spheres
The volume of the square pyramid is 6 cubic feet.
10. (See page 728 of your text.)
SOLUTION: The radius of the sphere is half the diameter, so 12 ÷ 2 = 6.
The volume of the sphere is about 904.8 cubic inches.
11. SOLUTION: The radius of the base is half the diameter, so 1.9 ÷ 2 = 0.95.
The volume of the cone is about 4.3 cubic inches.
12. pentagonal pyramid: base area 52 in2, height 12 in.
SOLUTION: The volume of the pentagonal pyramid is 208 cubic inches.
13. rectangular pyramid: length 3.5 feet, width 2 feet, height 4.5 feet
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The volume of the rectangular pyramid is 10.5 cubic feet.
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12-4 Volume of Pyramids, Cones and Spheres
The volume of the pentagonal pyramid is 208 cubic inches.
13. rectangular pyramid: length 3.5 feet, width 2 feet, height 4.5 feet
SOLUTION: The volume of the rectangular pyramid is 10.5 cubic feet.
14. cone: diameter 6.7 mm, height 2.1 mm
SOLUTION: The radius of the base is half the diameter, so 6.7 ÷ 2 = 3.35.
The volume of the cone is about 24.7 cubic millimeters.
15. sphere: radius 7.2 km
SOLUTION: The volume of the sphere is about 1563.5 cubic kilometers.
16. sphere: diameter 1.8 mm
SOLUTION: The radius of the sphere is half the diameter, so 1.8 ÷ 2 = 0.9.
The volume of the sphere is about 3.1 cubic millimeters.
17. WEATHER A cone-shaped icicle is 2.5 feet long and has a diameter of 1.5 feet.
a. Find the amount of ice in the icicle to the nearest tenth of a cubic foot.
b. The
icicle
melts by
at Cognero
a rate of 0.1 cubic foot every 5 minutes. How long will it take for the icicle to melt?
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SOLUTION: a.
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12-4 Volume of Pyramids, Cones and Spheres
The volume of the sphere is about 3.1 cubic millimeters.
17. WEATHER A cone-shaped icicle is 2.5 feet long and has a diameter of 1.5 feet.
a. Find the amount of ice in the icicle to the nearest tenth of a cubic foot.
b. The icicle melts at a rate of 0.1 cubic foot every 5 minutes. How long will it take for the icicle to melt?
SOLUTION: a. The radius of the base is half the diameter, so 1.5 ÷ 2 = 0.75.
The amount of ice in the icicle is about 1.5 cubic feet.
b. To find the amount of time it will take for the icicle to melt, use dimensional analysis.
It will take about 75 minutes or 1 hour 15 minutes for the icicle to melt.
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