You are filling up a cylindrical tank with a radius of 5m with water at a rate of 3 cm^3/min. Unbeknownst to you the tank has a hole and is leaking at a rate of 1 cm^3/min.

How fast is the height of the water increasing?

The volume of a cylinder V = πr^ (2) h.

dh/dt = 3/25π m/min

Step-by-step explanation:

Radius = 5m

Rate (dV/dt) = 3 cm^3 / min

Leaking rate = 1 cm^3 / min

Volume = πr^2h

Volume = π (5) ^2h

V = 25πh

Differentiate volume implicitly with respect to time

dV/dt = 3 cm^3/min

3 = 25π (dh/dt)

dh/dt = 3 m^3/min / 25πm^2

dh/dt = 3/25πm/min