Solve the Problem $r$ Increases at the Rate Of $0.04$ Inches Per Second and That

Multiple Choice

Solve the problem.
-A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius $r$ increases at the rate of $0.04$ inches per second and that $r = 33$ inches at time $t = 0$ . Determine the equation that models the volume $\mathrm { V }$ of the balloon at time $t$ and find the volume when $t = 310$ seconds.

A) $\mathrm { V } ( \mathrm { t } ) = \frac { 4 \pi ( 0.04 \mathrm { t } ) ^ { 3 } } { 3 } ; 23,959.34 \mathrm { in } ^ { 3 }$
B) $V ( t ) = \frac { 4 \pi ( 33 + 0.04 t ) ^ { 3 } } { 3 } ; 391,973.01 \mathrm { in } ^ { 3 }$
C) $V ( t ) = 4 \pi ( 33 + 0.04 t ) ^ { 2 } ; 1,306,170.68$ in. 3
D) $V ( t ) = 4 \pi ( 0.04 t ) ^ { 2 } ; 1932.21$ in.3