Question

A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of the silo (including the part inside the roof section) is 15,000 ft³ and the cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot? r = ___________ ft

Answer 1

To find the radius of the silo, we can use the formula V = πr²h and rearrange it to solve for the radius. By plugging in the given values for the volume and height of the cylindrical part, we can calculate the radius to be approximately 10.0 ft.

Step-by-step explanation:

To find the radius of the silo, we need to first calculate the volume of the cylindrical part using the formula V = πr²h. Since the total volume of the silo is given as 15,000 ft³ and the cylindrical part is 30 ft tall, we can rearrange the formula to solve for the radius:

15,000 = πr² × 30

r² = 15,000 / (30π)

r ≈ √(500 / π) ≈ 10.0 ft

Therefore, the radius of the silo is approximately 10.0 ft.