Question

A silo is a composite of a cylindrical tower with a cone for a roof. Find the volume of the silo if the

radius of the base is 120 feet, the height of the roof is 25 feet, and the height of the entire silo is 130

feet.

Answer 1

5127079.21 cubic feet

Explanation:

The silo is in the shape of a cylinder and a cone.

The volume of the silo will be the sum of the volumes of the cylinder and the cone.

Therefore, its volume is:

`V = \pi r^2h + (1)/(3) \pi rH`

where r = radius of cylinder and cone

h = height of cylinder

H = height of cone

The radius of the base is 120 feet, the height of the roof (cone) is 25 feet. The height of the entire silo is 130 feet. This means that the height of the cylinder is:

130 - 25 = 105 feet

Therefore, the volume of the silo is:

`V = (\pi * 120^2 * 105) + ((1)/(3) * 120^2 * 25)\\\\V = 4750088.09 + 376991.12\\\\V = 5127079.21 ft^3`

The volume of the silo is 5127079.21 cubic feet.