Question

The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to

time) when the height is 20 cm.
A. 36Pi
B. 108pi
C. 360pi
D. None of these

Answer 1

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