Question

A grain silo has the dimensions shown. (height of 60, diameter of 20). The top of the silo is a hemispherical shape. Find the volume of the grain silo.

Answer 1

Answer:

$20943.96 ft^3$

Step-by-step explanation:

The silo is shaped as a cylinder with a hemisphere on top of it.

We need to find the volume of the shape.

The volume of a cylinder is given as:

$V = \pi r^2h$

where r = radius

h = height

The volume of a hemisphere is given as:

$V = \frac{2}{3} \pi r^3$

where r = radius

Therefore, the joint volume of both shapes is:

$V = \pi r^2h + \frac{2}{3} \pi r^3$

The height of the silo is 60 and the diameter is 20.

This means that the radius is 10.

The cylindrical part of the silo and the hemispherical part have the same radius, 10.

The volume of the silo is:

$V = \pi * 10^2 * 60 + \frac{2}{3} * \pi * 10^3\\ \\V = 18849.56 + 2094.40\\\\V = 20943.96 ft^3$

The volume of the silo is $20943.96 ft^3$