SOLUTION: If the radius of a sphere is increasing at the constant rate of 3 millimeters per second, how fast is the volume changing when the surface area 4πr2 is 10 square millimeters?

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Question 1185753: If the radius of a sphere is increasing at the constant rate of 3 millimeters per second, how fast is the volume changing when the surface area 4πr2 is 10 square millimeters?

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The given information makes finding the answer easy, if you know the basic method for solving the problem.

V+=+%284%2F3%29%28pi%29r%5E3

dV%2Fdt+=+4%28pi%29%28r%5E2%29%28dr%2Fdt%29

The 4%28pi%29%28r%5E2%29 is given, so

dV%2Fdt+=+%2810%29%283%29+=+30

ANSWER: When the surface area is 10 square millimeters, the volume is increasing at a rate of 30 cubic millimeters per second.