1973 AMC 12 Problem 8

Question

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

90

72

45

30

15

Paint required scales with surface area, not volume

Reducing every length by a factor of

6

reduces the paint per statue by the square of that factor

A

1

-ft. statue has linear scale

\frac{1}{6}

relative to the original, so its surface area and paint requirement are

\frac{1}{36}

as large. The

540

small statues therefore require

540\cdot\frac1{36}=15

pints.

Therefore, the correct answer is E.

Problem 8 in other years