Question

A grain storage silo consists of a cylinder and a hemisphere. The diameter of the cylinder and the hemisphere is 20 feet. The cylinder is 150 feet tall.

Answer 1

GIven

the height of the cylinder is 150ft

diameter of hemisphere and the cylinder is 20ft

radius = d/2

then the height of hemisphere is equal to the radius of it

height of the hemisphere = 10

`\begin{gathered} \text{radius}=(20)/(2) \\ r=10 \end{gathered}`

volume of the silo = volume of the cylinder + volume of the hemisphere

first we find the volume of the cylinder

`\begin{gathered} \text{volume of the cylinder = }\pi r^2h \\ =\pi(10)^2(150) \\ =\pi100(150) \\ =15000\pi \end{gathered}`

now we find the volume of the hemisphere

`\begin{gathered} \text{volume of hemisphere =}(2)/(3)\pi r^3 \\ =(2)/(3)\pi(10)^3 \\ =(2)/(3)\pi(1000) \end{gathered}`

now we calculte the volume of the silo

`\begin{gathered} \text{volume of silo=}15000\pi+(2)/(3)\pi(1000) \\ =\pi(15000+(2)/(3)(1000)) \\ =\pi(15000+(2000)/(3))_{} \\ =\pi(15000+666.6) \\ =\pi(15666.6) \\ =(22)/(7)(15666.6) \\ =49237.8cubicft \end{gathered}`