The formula for the volume of a right cylinder is V = (pi)r^2h. Find the rate of change of the volume when r = 2 inches if dr/dt = 1/8 in./min and h = 5r. Show all your work.

The volume is increasing at a rate of 15π/2 squared inches per minute.

Step-by-step explanation:

The formula for the volume of a right cylinder is:

We want to find dV/dt when r = 2, dr/dt = 1/8 in/min, and h = 5r.

Since h = 5r:

Differentiate both sides with respect to t:

Since r = 2 and dr/dt = 1/8:

So, the volume is increasing at a rate of 15π/2 squared inches per minute.