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 9 inches per minute, and the height is decreasing at a rate of 7 inches per minute. What is the rate of change of the surface Area when the radius is 12 inches and the height is 32 inches?

A) $936 \pi \mathrm { in. } ^ { 2 } / \mathrm { min }$
B) $984 \pi$ in. $^ { 2 } / \mathrm { min }$
C) $876 \pi$ in. $^ { 2 } / \mathrm { min }$
D) $840 \pi$ in. $^ { 2 } / \mathrm { min }$
E) $968 \pi$ in. $^ { 2 } / \mathrm { min }$