Q: The volumes of two cylindrical cans of the same shape vary directly as the cubes of their radii. If a can with a six-inch radius holds 1½ pints, how many gallons will a similar can with a 24-inch

radius hold?

A: Solution:using 8 pints/gallon and S an unknown constant
vol varies as r^3 So
vol = S * r^3;
S*6^3 = 1.5;
S*24^3 = x ;
1.5 is to S*6^3 as x is to S*24^3
1.5/S*6^3 = x/S*24^3;
x = 1.5 * (24/6)^3;
x = (1.5 * 24^3)/6^3 = 1.5 * 4^3 = 96 pints;
96 [ pints * 1 gallon/8 pints = 12 gallons ]

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Asked 6/17/2013 5:25:33 PM

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