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Question

If 1 pint is needed to paint a statue 6 m high, then the number of pints it will take to paint (to the same thickness) 540 statues similar to the original but only 1 m high is

A
90
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B
72
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C
45
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D
15
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Solution

The correct option is D 15
The number of pints P of paint needed is proportional to the surface area (hence, to the square of the height h) of a statue and also to the number (n) of statues to be painted. Thus, p=knh2. Substituting n=1, h=6 and p=1 into this equation, we obtain the constant of proportionality k=136, so that p=136nh2
Now, when n=540, h=1, then p=136×540×12=15.

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