The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. what is the rate of change of the volume of the cylinder when the height is 20cm.

108π cm^3/min

Step-by-step explanation:

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

The volume of a cylinder;

V = π r^2 h

   = 36π h

differentiating both sides with respect to t;

dV/dt = 36π dh/dt

but dh/dt = 3 cm/min

dV/dt = 36π(3) = 108π cm^3/min