related rates (one forumla)

Question

The radius of a sphere is decreasing at a constant rate of 6 centimeters per minute. At the instant when the radius of the sphere is 66 centimeters, what is the rate of change of the volume? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V= 3 4 ​ πr 3 . Round your answer to three decimal places.

Answer 1

dr/dt = - 6 ; r = 66

V = 4/3πr³

dV/dt = 4πr²·dr/dt

dV/dt = - 328,434.662 cm³/min