One swimming pool is circular and another is rectangular. The rectangular pool's width is six times its depth. Its length is 12 feet more than its width. The circular pool has a diameter that is twice the width of the rectangular pool, and it is 2 feet deeper. Find the ratio of the circular pool's volume to the rectangular pool's volume.
A) $2 \pi$
B) $\pi$
C) $\frac { 1 } { \pi }$
D) $\pi ^ { 2 }$
E) $6 \pi$

Question

Quizplus · Accepted Answer

The volume of the rectangular pool is $ w \times 6w \times w = 6w^3 $. The circular pool's radius is $ w $, and its depth is $ w + 2 $, so its volume is $ \pi w^2 (w + 2) = \pi w^3 + 2\pi w^2 $. The ratio is $\frac{\pi w^3 + 2\pi w^2}{6w^3} = \frac{\pi + 2\pi/w}{6} \approx \pi$ when $w$ is large.

One Swimming Pool Is Circular and Another Is Rectangular 2π2 \pi2π

One Swimming Pool Is Circular and Another Is Rectangular $2 \pi$