Suppose that, for the sphere in the video, instead of being told how fast the radius is changing, we're told that the volume is increasing at a constant rate of d V d t = 4 cubic centimeters per second. How fast is the radius increasing at the instant when the radius is r = 10 centimeters? d r d t =

Question

Physics

Ann Mitchell

28 April, 16:47

Suppose that, for the sphere in the video, instead of being told how fast the radius is changing, we're told that the volume is increasing at a constant rate of d V d t = 4 cubic centimeters per second. How fast is the radius increasing at the instant when the radius is r = 10 centimeters? d r d t =

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Answers (1)

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Andres Yu · Answer 1

3.185 x 10^-3 cm/s

Explanation:

dV / dt = 4 cubic cm per second

r = 10 cm

The volume of sphere is given by

V = 4/3 x π x r³

Differentiate both sides with respect to t

dV / dt = 4/3 x π x 3r² x dr/dt

Put dV / dt = 4 cubic cm per second, r = 10 cm

4 = 4/3 x 3.14 x 3 x 10 x 10 x dr/dt

dr/dt = 3.185 x 10^-3 cm/s