The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when inches.Round your answer to one decimal place.

Question

The radius r of a sphere is increasing at a rate of 5 inches per minute.Find the rate of change of volume when  inches.Round your answer to one decimal place. ​

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr³.

Taking the derivative with respect to time, we get:

dV/dt = 4πr² (dr/dt)

Substituting the given values, we get:

dV/dt = 4π(11)² (5)

dV/dt = 9,047.8 cubic inches per minute (rounded to one decimal place)

Therefore, the answer is choice D.

The Radius R of a Sphere Is Increasing at a Rate