The height of a cylinder with a fixed radius of 10 cm is increasing at the rate of 0.5 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 30cm.

Answer 1

v = pi r^2 h = 100pi h
dv/dt = 100pi dh/dt

Now just plug in your numbers to get dv/dt.

Note that it does not matter what the height is. Since the cylinder has a constant radius, its volume is directly proportional to its height.