Posted by Greg on Friday, March 2, 2012 at 3:07pm.
Luckily, all we are working with is a triangular section, until the water is 5' deep; then we have to work with a trapezoid.
Anyway, looking at the side of the pool, when the water is y' deep, we have a triangular prism with a cross-section that is y by y/8 (since the pool bottom is a line with slope 5/40 = 1/8
So, the volume is
v = 1/2 * y*y/8 * 20 = 5y^2/4
dv/dt = 5y/2 dy/dt
40 = 5*3/2 dy/dt
dy/dt = 16/3 ft/min
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