Solve the Problem $V ( r ) = \pi ( 66 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }$

Multiple Choice

Solve the problem.
-A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r. A) $V ( r ) = \pi ( 66 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }$
B) $\mathrm { V } ( \mathrm { r } ) = \pi ( 66 - \mathrm { r } ) + \frac { 4 } { 3 } \pi \mathrm { r } ^ { 2 }$
C) $V ( r ) = \pi ( 66 - r ) r ^ { 3 } + \frac { 4 } { 3 } \pi r ^ { 2 }$
D) $V ( r ) = 66 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$