Math CentralQuandaries & Queries


Question from David, a student:

A circular swimming pool with a diameter of 30ft and a horizontal bottom contains 22,000 gal of water. What is the depth of the water in the pool? (one cubic foot contains approximately 7.5 gal of water.)

I'm having a great deal of problem dealing with this, i don't know if the equation I'm using is correct or am i plugging it in the wrong place. V=TTr^2h .
if you can could you please explain to me step by step on how to set up this problem? the horizontal bottom thrown me off the most

Hi David,

You are using the correct expression for the volume. The shape is a right circular cylinder.

First you need to convert the 22,000 gallons into cubic feet. Using your 7.5 gallons per cubic foot, 22,000 gallons is 22,000/7.5 cubic feet. The diameter of the pool is 30 feet so its radius r is 15 feet. Substitute these values into the expression

V = π r2 h

and solve for h, the height of the water.


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