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)πr^3

We need to find the rate of change of volume, so we need to differentiate both sides with respect to time:

dV/dt = 4πr^2 (dr/dt)

Now we substitute the given values and solve:

r = 11 inches
dr/dt = 5 inches per minute

dV/dt = 4π(11)^2(5) = 9,047.8 cubic inches per minute

Therefore, the answer is D.

The Radius R of a Sphere Is Increasing at a Rate