A storage tank has a Diameter of 20ft and a height of 10ft. The output volumetric flow from this tank is given by


where h(t) is the height of the liquid in the tank. At a particular time the tank is at steady state with an input flow of 10ft3/min.

What is the steady-state liquid height in the tank?

If the input flow rate is ramped up at a rate of 0.1ft3/min how many minutes will it take the tank to over flow?

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