The Radius of a Right Circular Cylinder Is Increasing at a Rate

Multiple Choice

The radius of a right circular cylinder is increasing at a rate of 6 inches per minute, and the height is decreasing at a rate of 4 inches per minute. What is the rate of change of the volumeWhen the radius is 14 inches and the height is 32 inches?

A) $4480 \pi$ in $^ { 3 } / \mathrm { min }$
B) $5488 \pi$ in $^ { 3 } / \mathrm { min }$
C) $4920 \pi$ in $^ { 3 } / \mathrm { min }$
D) $4592 \pi$ in $^ { 3 } / \mathrm { min }$
E) $4928 \pi$ in $^ { 3 } / \mathrm { min }$