1955 AMC 12 Problem 15

Attempt Problem 15 of the 1955 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1955 AMC 12 solutions, or check the answer key.

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15.

The ratio of the areas of two concentric circles is

1:3.

If the radius of the smaller is

r,

then the difference between the radii is best approximated by:

0.41r

0.73

0.75

0.73r

0.75r

Area ratios are the squares of radius ratios

The larger radius is

r\sqrt3

, so estimate

\sqrt3-1

If the larger radius is

R,

then

\frac{\pi r^2}{\pi R^2}=\frac13,

R=r\sqrt3.

The difference is

R-r=(\sqrt3-1)r\approx0.732r.

Thus, the best approximation is

0.73r,

and the correct answer is D.

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