1951 AMC 12 Problem 6

Attempt Problem 6 of the 1951 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 1951 AMC 12 solutions, or check the answer key.

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

The bottom, side, and front areas of a rectangular box are known. The product of these areas is equal to:

The volume of the box

The square root of the volume

Twice the volume

The square of the volume

The cube of the volume

Call the three edge lengths

l,w,h

Multiply the three face areas

lw,

wh,

and

hl

If the edge lengths are

l,w,h,

the three face areas are

lw,

wh,

and

hl.

Their product is

(lw)(wh)(hl)=l^2w^2h^2=(lwh)^2,

the square of the volume.

Thus, the correct answer is D.

Problem 6 in other years