1973 AHSME Problems/Problem 8

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Problem

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

$\textbf{(A)}\ 90\qquad\textbf{(B)}\ 72\qquad\textbf{(C)}\ 45\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 15$

Solution

The statues are similar, and since the height if the smaller statue is $\tfrac{1}{6}$ of the original statue, the surface area is $\tfrac{1}{36}$ of the original statue. Thus, $\tfrac{1}{36}$ pints of paint is needed for one 1 ft. statue, so painting 540 of these statues requires $\tfrac{540}{36} = \boxed{\textbf{(E)}\ 15}$ pints of paint.

See Also

1973 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 7
Followed by
Problem 9
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