Choose the one alternative that best completes the statement or answers the question.
-A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the radius of the hemisphere is 10 feet and the height of the silo is heet, express the volume of the silo as a function of h.
A) $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$
B) $\mathrm { V } ( \mathrm { h } ) = 4100 \pi ( \mathrm { h } - 10 ) + \frac { 500 } { 7 } \pi$
C)$ \mathrm { V } ( \mathrm { h } ) = 100 \pi \mathrm { h } + \frac { 4000 } { 3 } \pi \mathrm { h } ^ { 2 }$
D) $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$

Question

Quizplus · Accepted Answer

The volume of the silo can be expressed as 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 $r = 10$ feet and $h$ is the height of the cylindrical part. The volume of the hemisphere is given by $V_{hemisphere} = \frac{2}{3} \pi r^3$, where $r = 10$ feet. Therefore, the total volume of the silo is $V(h) = \pi (10)^2 (h - 10) + \frac{2}{3} \pi (10)^3$, simplifying to $V(h) = 100\pi (h - 10) + \frac{2000}{3}\pi$.

Choose the One Alternative That Best Completes the Statement or Answers