SOLUTION: the radius r of a sphere is increasing at a rate of 2 inches per minute. find the rate of change of the volume when r=6 inches and dr/dt=24 inches.

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: the radius r of a sphere is increasing at a rate of 2 inches per minute. find the rate of change of the volume when r=6 inches and dr/dt=24 inches.      Log On


   

Question 14136: the radius r of a sphere is increasing at a rate of 2 inches per minute. find the rate of change of the volume when r=6 inches and dr/dt=24 inches.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
V+=+%284%2F3%29%2Api%2Ar%5E3
dV%2Fdr+=+4%2Api%2Ar%5E2

Now, %28dV%2Fdt%29+=+%28dV%2Fdr%29%2A%28dr%2Fdt%29 --> confirm, by cancelling the dr terms on the right.

so, we have dV/dr, when r=6 --> find dV/dr.
We also know dr/dt --> 2

So we can find dV/dt.

I do not know what the 24 is though... you say it is dr/dt...the rate of change of r, but that is 2, in the question.

Please check your question.

jon.