Question

The radius of a right circular cylinder is increasing at a rate of 2 units per second. The height of the cylinder is decreasing at a rate of 5 units per second. Which of the following expressions gives the rate at which the volume of the cylinder is changing with respect to time in terms of the radius r and height h of the cylinder?.

Answer 1

dV/dt = π (4rh - 5r^2)

Step-by-step explanation:

Volume V = π r^2*h

dV/dt = π * (2r*dr/dt * h + r^2 *dh/dt)

Given dr/dt = 2. dh/dt = -5

so

dV/dt = π (4rh - 5r^2)