The Volume of a Conical Pile of Sand Is Increasing $576 \pi$

Multiple Choice

The volume of a conical pile of sand is increasing at a rate of $576 \pi$ ft ³ /min, and the height of the pile always equals the radius r of the base. Express r as a function of time t (in minutes) , assuming that r = 0 when t = 0.

A) $r = 12 \sqrt [ 3 ] { t }$
B) $r = \sqrt [ 3 ] { 576 \pi t }$
C) $r = \sqrt [ 3 ] { 12 t }$
D) $r = 576 \pi \sqrt [ 3 ] { t }$
E) $r = 576 \sqrt [ 3 ] { \pi t }$