The Two Radii of the Frustum of a Right Circular $7,275 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$

Multiple Choice

The two radii of the frustum of a right circular cone are increasing at a rate of 4 centimeters per minute, and the height is increasing at a rate of 12 centimeters per minute (see figure) . Find the rate at which the volume is changing when the two radii are 15 centimeters and 30 Centimeters, and the height is 10 centimeters.

A) $7,275 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$
B) $8,100 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$
C) $8,250 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$
D) $4,800 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$
E) $7,650 \pi \mathrm { cm } ^ { 3 } / \mathrm { min }$