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) $V ( r ) = 66 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$

Question

Quizplus · Accepted Answer

The volume of the silo is the sum of the volume of the cylinder and the volume of the hemisphere. The volume of the cylinder is given by $V_{cylinder} = \pi r^2 h$, where $h = 66 - r$ (since the total height is 66 feet and the hemisphere's height is $r$, so the height of the cylindrical part is $66 - r$). The volume of the hemisphere is given by $V_{hemisphere} = \frac{2}{3}\pi r^3$. Therefore, the total volume $V(r)$ is $V(r) = \pi (66 - r)r^2 + \frac{2}{3}\pi r^3$.

Solve the Problem V(r)=π(66−r)r2+23πr3V ( r ) = \pi ( 66 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }V(r)=π(66−r)r2+32​πr3

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