1978 AMC 12 Problem 2

Attempt Problem 2 of the 1978 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 1978 AMC 12 solutions, or check the answer key.

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

If four times the reciprocal of the circumference of a circle equals the diameter of the circle, then the area of the circle is

\frac1{\pi^2}

\frac1\pi

1

\pi

\pi^2

Write the circumference and diameter in terms of the radius

r

The condition directly determines the product

\pi r^2

The condition is

4\left(\frac1{2\pi r}\right)=2r.

Multiplying by

\pi r

gives

2=2\pi r^2,

so the area

\pi r^2

equals

1.

Therefore, the correct answer is C.

Problem 2 in other years