Swimming Pool VolumeDate: 02/28/2002 at 11:16:54 From: David Strong Subject: Cubic feet vs gallons. What formula would I use to calculate the volume of a swimming pool 135' x 70' with different depths of 3', 5', 8' and 11'? Thanks, DS Date: 02/28/2002 at 12:36:27 From: Doctor Peterson Subject: Re: Cubic feet vs gallons. Hi, David. It's not quite clear exactly what shape the pool is; I presume it doesn't just drop off suddenly from one depth to another, but slopes down from one level to another. Suppose the cross-section looks like this, with straight lines within each section: a b c d +-------+---------+-----------+------+ |r | | | | | |s | | | + | |t | | \ | | |u |v +_____ | | | ----+ | | \ | | \ | | +------+ The area of this cross-section will be the sum of four trapezoids, each of whose areas is its "height" (width in this case) times the average of its two "bases" (depths in this case). The volume of the pool is the product of that area and the width perpendicular to this cross-section. So the volume will be V = w[a(r+s)/2 + b(s+t)/2 + c(t+u)/2 + d(u+v)/2] This can be rewritten as V = w/2 * [ar + (a+b)s + (b+c)t + (c+d)u + dv] If the measurements are all in feet, this will give cubic feet. To convert to gallons, multiply by 12^3 = 1728 to get cubic inches, and divide by 231 cubic inches per gallon. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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