PROBLEMS INVOLVING VOLUME
EXAMPLE 2.7.1
| The pedestal on which a statue is raised is a rectangular concrete solid
measuring 9 feet long, 9 feet wide and 6 inches high.
How much is the cost of the concrete in the pedestal, if concrete costs $70 per cubic yard? A. $34,020 B. $105 C. $315 D. $2835 | 
|
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EXAMPLE 2.7.2
Gomer stores his iguana food in a can that is 8 inches tall and has a diameter of 6 inches. He stores his hamster food in a can that is 10 inches tall and has a diameter of 5 inches.
Which can is larger?
A. The iguana food can.
B. The hamster food can.
C. They are the same size.
D. There is insufficient information to answer this question.
see solution
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EXAMPLE 2.7.3
Gomer has a super-jumbo-sized drip coffee maker. The beverage is produced as hot water filters through a cone-shaped vessel containing coffee grounds (see diagram below)
Assuming that the cone is filled with water,
and the water is dripping out at a rate of 10 cu. in. per minute,
how long will it take for all of the water to pass through?
see solution
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EXAMPLE 2.7.4
Gomer has been working out by lifting weights. He finds that a spherical lead-alloy weight with a radius of 3 inches weighs 20 pounds. He wishes to lift 100 pounds, so he special-orders a spherical weight with a radius of 15 inches. Why is Gomer in intensive care?
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EXAMPLE 2.7.5
The radius of the Earth is about 4000 miles. The radius of the Sun is about 400,000 miles. How many times bigger than the Earth is the Sun?
A. 10
B. 100
C. 1,000
D. 1,000,000
see solution
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EXAMPLE 2.7.6
Gomer has noticed that when a garden hose is left exposed to the summer sunshine, the water resting within the hose becomes heated. This inspires Gomer to construct a low-tech solar water heater. He reasons that if he connects a sufficient length of hose and leaves it in a sunny spot, this will provide an ample supply of hot water.
He estimates that the drum of his washing machine is a cylinder whose diameter is 17 inches and height is 10 inches. Based on that assumption, how many lineal feet of half-inch diameter water hose would be required in order to hold enough water to fill the drum of the washing machine?
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EXAMPLE 2.7.7
Gomer delivers muffins for the Muffin-O-Matic muffin company. Each muffin is packed in its own little box. An individual muffin box has the shape of a cube, measuring 3 inches on each side. Gomer packs the individual muffin boxes into a larger box. The larger box is also in the shape of a cube, measuring 2 feet on each side. How many of the individual muffin boxes can fit into the larger box?
A. 8
B. 16
C. 64
D. 512
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see solution
EXAMPLE 2.7.8
To determine the number (N) of 5-pound bags of ice required to reduce the temperature of water in a swimming pool by Dº Fahrenheit, use the formula N = 0.06125DV, where V is the volume of the pool (in cubic feet). Gomer has a circular pool with a diameter of 12 feet, filled to a depth of 3 feet. How many 5-pound bags of ice are required to reduce the pool's temperature from 85º to 80º Fahrenheit?
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