The radius r of a sphere is increasing at a rate of inches per minute. Find the rate of change of the volume when r = inches.

Question

The radius r of a sphere is increasing at a rate of  inches per minute. Find the rate of change of the volume when r =  inches.

Quizplus · Accepted Answer

The volume of a sphere is given by V = (4/3)πr^3.
Taking the derivative with respect to time, we have:
dV/dt = 4πr^2(dr/dt)
Substituting r = 11, dr/dt = 11eaa595_6613_6aae_a696_f513d65ebb99_TB4584_11_TB4584_11, we get:
dV/dt = 4π(11)^2(11eaa595_6613_6aae_a696_f513d65ebb99_TB4584_11_TB4584_11)
Simplifying, we get:
dV/dt = 11eaa595_6613_b8d2_a696_d11b44bcce47_TB4584_11_TB4584_11
Therefore, the rate of change of the volume when r = 11eaa595_6613_6aaf_a696_4957f294b079_TB4584_11_TB4584_11 inches is 11eaa595_6613_b8d2_a696_d11b44bcce47_TB4584_11_TB4584_11 cubic inches per minute, which is option C.

The Radius R of a Sphere Is Increasing at a Rate