$\text { The radius of a right circular cylinder is } \sqrt { 3 t + 6 } \text { and its height is } t ^ { 5 } \text {, where } t \text { is }$

Multiple Choice

$\text { The radius of a right circular cylinder is } \sqrt { 3 t + 6 } \text { and its height is } t ^ { 5 } \text {, where } t \text { is }$ time in seconds and the dimensions are in inches. Find the rate of change of the volume of the cylinder, V, with respect to time.

A) $\frac { d V } { d t } = \pi t ^ { 4 } ( 30 + 15 t )$ cubic inches per second
B) $\frac { d V } { d t } = \pi t ^ { 4 } ( 30 + 18 t )$ cubic inches per second
C) $\frac { d V } { d t } = \pi t ^ { 3 } ( 30 + 18 t )$ cubic inches per second
D) $\frac { d V } { d t } = \pi t ^ { 4 } ( 6 + 18 t )$ cubic inches per second
E) $\frac { d V } { d t } = \pi t ^ { 5 } ( 30 + 18 t )$ cubic inches per second