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.
A) 1,809.6 cubic inches per minute
B) 7,238.2 cubic inches per minute
C) 36,191.1 cubic inches per minute
D) 9,047.8 cubic inches per minute
E) 27,143.4 cubic inches per minute

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. ​
A) 1,809.6 cubic inches per minute 
B) 7,238.2 cubic inches per minute 
C) 36,191.1 cubic inches per minute 
D) 9,047.8 cubic inches per minute 
E) 27,143.4 cubic inches per minute

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