(Solved): The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decrea ...

The radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.7 in/s. At what rate is the volume of the cone changing when the radius is 192 in. and the height is 197 in.? Step 1 The volume of a cone with base radius r and height h is given by V = [ter2h. r V = = . To find the rate of change of the volume, we need to find dV By the Chain Rule, we know that dt av av dh dV dt dr + dt a a 1 h dt r h Step 2 We are given that dr = 1.6 and dt dh dt = -2.7. Also, av ar - arh 2 trh and av an = ???? ??2 3 Step 3 When r = 192 and h = 197, then = = av ar and av ah