Water is pouring into a cylinder with a radius of 5m and height of 20m at a rate of 3 cubic metres a minute. Find the rate of change of height when the tank is half full.
Now the Volume V = $πr^2h$ and I can determine the rate of change in Volume is $dV/dt = πr^2dh/dt$ and the rate of change of height is $dh/dt = 1/πr^2\times dV/dt$
Using that formula I can determine that the water is rising at a rate of $3/25π$ m/min. But I cannot seem to figure out how to factor in height so that it is half full. Or is this wrong?