Posted by **joseph** on Thursday, December 27, 2012 at 11:15pm.

A water heater in the shape of a circular cylinder is standing vertically, resting on one of the round ends. The tank is 60 inches tall and has a volume of 30 gallons. If water is flowing into the tank at the rate of 5 gallons per minute, at what rate is the level of the water in the tank increasing?

- calculus -
**Steve**, Thursday, December 27, 2012 at 11:30pm
the volume of a 1" layer of water is 1/2 gal. So, when the height of the water is h inches, the volume of water is

v = 1/2 h

dv/dt = 1/2 dh/dt

5 = 1/2 dh/dt

so,

dh/dt = 10 in/min

You can go through all that pi r^2 stuff, but it's not needed here.

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