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January 29, 2015

January 29, 2015

Posted by **Lost** on Thursday, December 20, 2012 at 4:09pm.

What is the equation for finding the rate at which the water level is rising?

- Calculus -
**Steve**, Thursday, December 20, 2012 at 4:21pmIf the water is at depth y<12, the cross-section of the water seen from the side of the pool is a triangle. The length of the water surface is y/12 * 60.

So, the volume of water is

v = 1/2 * y/12 * 60 * y * 25 = 125/2 y^2

dv/dt = 125y dy/dt

so, at depth y=5,

800 = 125(5) dy/dt

dy/dt = 1.28 ft/min

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