Question

Water is being pumped into a leaky inverted conical tank at a rate of 10 m3/h. The tank has a height of 9 m and the diameter at the top is 6 m. If the water level is rising at a rate of 0.2 m/h when the height of the water is 6 m, how fast is the water leaking out at that time? [Recall: The volume of a cone is π/3 r^2 h

Answer #1

Given and .

Thus

Voulme of cone is given by

Using chain rule we get

Let be the volume of water being pumped in and be the volume of water leaking out. Then

We are given

Thus

Thus, the water leaking out at the rate of .

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