A Water Tank Is Formed by Revolving the Curve $y = 3 x ^ { 4 }$

Multiple Choice

A water tank is formed by revolving the curve $y = 3 x ^ { 4 }$ about the $y$ -axis. Water drains from the tank through a small hole in the bottom of the tank. At what constant rate does the water level, $y$ , fall? (Use Torricelli's Law: $\mathrm { dV } / \mathrm { dt } = - \mathrm { m } \sqrt { \mathrm { y } }$ .)

A) $\frac { d y } { d t } = \frac { - m \pi } { \sqrt { 3 } }$
B) $\frac { d y } { d t } = \frac { - \sqrt { 3 } } { m \pi }$
C) $\frac { \mathrm { dy } } { \mathrm { dt } } = \frac { - \pi } { \mathrm { m } \sqrt { 3 } }$
D) $\frac { \mathrm { dy } } { \mathrm { dt } } = \frac { - \mathrm { m } \sqrt { 3 } } { \pi }$