The radius r of a sphere is increasing at a rate of 3 inches per minute. Find the rate of change of volume when r = 17 inches. Round your answer to one decimal place.
A)3631.7 cubic inches per minute
B)20,579.5 cubic inches per minute
C)61,738.6 cubic inches per minute
D)10,895.0 cubic inches per minute
E)32,685.1 cubic inches per minute

Question

Quizplus · Accepted Answer

The formula for the volume of a sphere is V = (4/3)πr^3. Taking the derivative with respect to time, we get dV/dt = 4πr^2 (dr/dt). When r = 17 inches and dr/dt = 3 inches per minute, we can plug in these values and solve for dV/dt: dV/dt = 4π(17)^2(3) = 10,895.0 cubic inches per minute. Therefore, the answer is D.

The Radius R of a Sphere Is Increasing at a Rate