Question

Suppose the radius, height and volume of a right circular cylinder are denoted as r, h, and V . The radius and height of this cylinder are increasing as a function of time. If dr/dt = 2 and dV/dt = 10π when r = 1, h = 2, what is the value of dh/dt at this time?

Answer 1

we know that volume of a right circular cylinder with radius r and height h is given by,

differentiate both the side with respect to t we can write,

we have to find dh/dt when r = 1 and h = 2 given that dr/dt = 2 and dV/dt = 10pi hence.