Solve the problem.
-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 h feet, express the volume of the silo as a function of h.
A) $V ( h ) = 4100 \pi ( h - 10 ) + \frac { 500 } { 7 } \pi$
B) $V ( h ) = 100 \pi h + \frac { 4000 } { 3 } \pi h ^ { 2 }$
C) $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$
D) $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$

Question

Solve the problem.
-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 h feet, express the volume of the silo as a function of h. 
A) $V ( h ) = 4100 \pi ( h - 10 ) + \frac { 500 } { 7 } \pi$
B) $V ( h ) = 100 \pi h + \frac { 4000 } { 3 } \pi h ^ { 2 }$
C) $V ( h ) = 100 \pi \left( h ^ { 2 } - 10 \right) + \frac { 5000 } { 3 } \pi$
D) $V ( h ) = 100 \pi ( h - 10 ) + \frac { 2000 } { 3 } \pi$

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 $V_{cylinder} = \pi r^2 h = \pi (10)^2 h = 100\pi h$. The volume of the hemisphere is $V_{hemisphere} = \frac{2}{3} \pi r^3 = \frac{2}{3} \pi (10)^3 = \frac{2000}{3} \pi$. Therefore, the total volume of the silo is $V(h) = 100\pi h + \frac{2000}{3} \pi$, but since the height of the cylinder part is $h - 10$ (not the total height $h$), the correct expression is $V(h) = 100\pi (h - 10) + \frac{2000}{3} \pi$.

Solve the Problem V(h)=4100π(h−10)+5007πV ( h ) = 4100 \pi ( h - 10 ) + \frac { 500 } { 7 } \piV(h)=4100π(h−10)+7500​π

Solve the Problem $V ( h ) = 4100 \pi ( h - 10 ) + \frac { 500 } { 7 } \pi$