1953 AMC 12 Problem 12

Attempt Problem 12 of the 1953 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 1953 AMC 12 solutions, or check the answer key.

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12.

The diameters of two circles are

8

inches and

12

inches respectively. The ratio of the area of the smaller to the area of the larger circle is:

\dfrac23

\dfrac49

\dfrac94

\dfrac12

none of these

Circle areas scale as the squares of their diameters

Square the diameter ratio

\frac{8}{12}

The area ratio is the square of the diameter ratio:

\left(\frac8{12}\right)^2=\left(\frac23\right)^2=\frac49.

Thus, the correct answer is B.

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