Question

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A conical tank in the shape of an inverted cone is being emptied from a valve at the bottom, at the rate of 3 cubic meters per min. The tank is 16 meters tall and the diameter of its circular top is 10 meter. Find the rate at which the water level is changing at the instant when the water is 9 meters deep.

Answer 1

The smaller and larger triangles are similar.
Therefore, r/h = 5/16 or r = 5/16h.
This gives the radius r as a function of height h.

Volume V = 1/3 * pi * r^2 * h
put r = 5/16*h in V and you will have V as a function of h.
Find dV/dt as a function of dh/dt
put dv/dt = -3 m^3/min and you will get a dh/dt in m/min.