1968 AMC 12 Problem 1

Attempt Problem 1 of the 1968 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 1968 AMC 12 solutions, or check the answer key.

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

Let

P

units be the increase in the circumference of a circle resulting from an increase of

\pi

units in the diameter. Then

P

equals:

\dfrac1\pi

\pi

\dfrac{\pi^2}{2}

\pi^2

2\pi

Write circumference as

\pi d

Replace

d

d+\pi

and subtract

The original circumference is

\pi d.

After the diameter increases by

\pi,

it is

\pi(d+\pi).

The increase is therefore

\pi(d+\pi)-\pi d=\pi^2.

Therefore, the correct answer is D.

Problem 1 in other years