1962 AMC 12 Problem 5

Attempt Problem 5 of the 1962 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 1962 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

If the radius of a circle is increased by

1

unit, the ratio of the new circumference to the new diameter is:

\pi+2

\dfrac{2\pi+1}{2}

\pi

\dfrac{2\pi-1}{2}

\pi-2

Call the new radius

R

Divide the circumference

2\pi R

by the diameter

2R

For every circle, regardless of its radius, the circumference divided by the diameter is

\frac{2\pi R}{2R}=\pi.

Thus, the correct answer is C.

Problem 5 in other years