Question

The roof of a grain silo is in the shape of a cone. The inside radius is 20 feet, and the roof is 10 feet tall. Below the cone is a cylinder 30 feet tall, with the same radius.

(If possible please explain premise, detail, conclusion!) Thanks!

Answer 1

Answer:

41887.90 cubic feet

Step-by-step explanation:

We need to find the volume of the silo.

We simply need to find the volume of the cylindrical part and the conical part and add them together.

The body of the silo is a cylinder with height of 30 ft and radius of 20 ft and the roof is a cone with height 10 ft and radius 20 ft.

The volume of a cylinder is given as:

$V = \pi r^2h$

The volume of a cone is given as:

$V = \frac{1}{3} \pi r^2H$

where r = radius of cylinder and cone

h = height of cylinder

H = height of cone

Adding them together, we have that the volume of the silo is:

$V = \pi r^2h + \frac{1}{3} \pi r^2H$

$V = \pi r^2 (h + \frac{1}{3}H)\\ \\V = \pi * 20^2 (30 + [\frac{1}{3}* 10]) \\\\V = 1256.64 ( 30 + 3.33)\\\\V = 1256.64(33.33)\\\\V = 41887.90 ft^3$

The volume of the silo is 41887.90 cubic feet.