Math CentralQuandaries & Queries


Question from tina:

How much water does a 24' round, 4' deep swimming pool hold?

Hi Tina,

The volume (amount of water the pool can hold) can be found by multiplying the area of base of the pool by the height. I'm not sure if the 24' refers to the diameter (distance across) or the circumference (distance around) of your pool, so I'll give you two answers:

1) If 24' is the diameter, then the area of the base of the pool, which in your case is a circle, is given by:  Area = Pi x ( diameter/2 )2 = Pi x (24/2)2 = Pi x144 ≈ 452.4 square feet
 So then:
 Volume ≈ 452.4 x 4 = 1809.6 cubic feet.

 So the pool can hold about 1809.6 cubic feet of water.

2) If 24' is the circumference of the pool, then we can use the circumference to find the radius, and then the radius to find the area of the base of the pool:

 Circumference = 2 x Pi x radius
 So then,
 radius = circumference / ( 2 x Pi ) = 24 / (2 x Pi ) = 12/Pi ≈ 3.82 feet
 And thus,
 area = Pi x radius2Pi x 3.822 = 45.8 square feet
 Then we have,
 Volume = (area of base) x height = 45.8 x 4 = 183.2 cubic feet.

 So the pool can hold about 183.2 cubic feet of water.








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