Question

You work for a store that sells built-to-order water reservoirs. Your manager asks you to visit a small business to measure a damaged conical water reservoir for replacement. The label on the water reservoir indicates only the following specifications: The height is 8.5 feet, and, when full, the water reservoir holds 225 cubic feet of water.Which formula will determine the radius of the water reservoir? Rounded to the nearest hundredth of a foot, what is the radius of the water reservoir?

Answer 1

• r = √(3V/(πh))
• r ≈ 5.03 feet

Explanation:

The volume of a cone is given by the formula ...

V = (1/3)πr²h

This formula can be used to find the radius, or we can rearrange it to solve for the radius:

3V = πr²h . . . . multiply by 3

(3V)/(πh) = r . . divide by the coefficient of r²

r = √(3V/(πh)) . . . . take the square root

__

We can fill in the given values to find the radius.

r = √(3·225/(π·8.5)) = √(1350/(17π)) ≈ 5.03 . . . . feet