The height of a cylinder with a fixed radius of 4 cm is increasing at the rate of 2 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is 14cm.

Answer 1

At a time of t minutes, let the height be h cm

V = π r^2 h = 16π h

dV/dt = 16π dh/dt
but dh/dt = 2 cm/min , and the height is not an issue, since the variable h does not appear in dV/dt

dV/dt = 16π(2) = 32π cm^3/min