Swimming Pool VolumeDate: 07/26/2001 at 03:50:21 From: Jim Majo Subject: Swimming pool volume How many gallons will an above-ground 24-foot-diameter pool 48 inches tall hold? Date: 07/26/2001 at 10:52:01 From: Doctor Paul Subject: Re: Swimming pool volume The figure you have described is a right circular cylinder. This page in our Dr. Math Formulas FAQ http://mathforum.org/dr.math/faq/formulas/faq.cylinder.html#rccylinder tells you that the formula for the volume is: V = Pi * r^2 * h Here, r = 12 feet (the radius is half the diameter) and h = 4 feet. So the volume is Pi * 12^2 * 4 = 1809.6 ft^3 Now - how many gallons of water will fit into this pool? We need to know how many cubic feet of water will fit into one gallon. I didn't know this answer off the top of my head, but I found this answer in our archives: Weight of a Gallon of Water http://mathforum.org/dr.math/problems/harris.7.29.99.html So it seems that 1 gallon = 3785.4 cm^3 That's almost what we need. We need a conversion between gallons and ft^3. So maybe we can convert cm^3 to ft^3. Since 1 ft = 30.48 cm, we have 1 ft^3 = 30.48^3 cm^3 = 28316.8 cm^3 So we can write: 1809.6 ft^3 28316.8 cm^3 1 gallon ----------- * ------------ * ----------- = 1 1 ft^3 3785.4 cm^3 13536.8 gallons of water. So it looks as if your pool will hold about 13,500 gallons of water. I hope this has been clear. Please write back if you have questions about how I arrived at any of the above conclusions. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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