1950 AMC 12 Problem 8

Attempt Problem 8 of the 1950 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 1950 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

100\%,

the area is increased:

100\%

200\%

300\%

400\%

By none of these

An increase of

100\%

doubles the radius

Circle area is proportional to the square of the radius

Increasing

r

100\%

changes it to

2r.

The area changes from

\pi r^2

\pi(2r)^2=4\pi r^2,

an increase of

3\pi r^2.

This is

300\%

of the original area.

Thus, the correct answer is C.

Problem 8 in other years