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

Multiple Choice

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s. At what rate is the volume of the cone changing when the radius is $108$ in. and the height is $132$ in.?

A) $108316.24 \mathrm { in } ^ { 3 } / \mathrm { s }$
B) $105316.24 \mathrm { in } ^ { 3 } / \mathrm { s }$
C) $111316.24 \mathrm { in } ^ { 3 } / \mathrm { s }$
D) $102316.24 \mathrm { in } ^ { 3 } / \mathrm { s }$
E) $99316.24 \mathrm { in } ^ { 3 } / \mathrm { s }$