Question

The radius of a right circular cylinder is decreasing at a rate of 2 inches per minute while the height is increasing at a rate of 8 inches per minute. determine the rate of change of the volume when r = 5 and h = 7.

Answer 1

V(t) = πr^2h
V'(t) = π(2rr'h + r^2h')
V'(t) = π(2(5)(-2)(7) + 5^2(8)
V'(t) = π(-140 + 200)
V'(t) = 60π in^3