The radius of a cylinder is increasing at the rate of 2 ~m / s and its height is decreasing at the rate of 3 ~m / s . When the radius is 3 m and height is 5 m , then the volume of the cylinder would change at the rate of

Step-by-step solution

Given, d r d t =2 ~m / s ....(i) d h d t =-3 ~m / s aligned Volume of cylinder, V & = r^2 h & d V d t & = [2 r h d r d t +r^2 d h d t ] aligned At r=3 ~m and h=5 ~m , d V d t = [2 3 5 2-9 3] [using Eq. (i) ] d V d t = [60-27]=33 d V d t =33 ~m ^3 / s