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The radius of a right circular cylinder is increasing at the rate of 2 in/min and the height is decreasing at a rate of 3 in/min. A) At what rate is the volume changing when the radius is 8 in and the height is 12 in? B) Is the volume increasing or decreasing?

Mathematics
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Volume = pi * radius^2 * height Derive wrt time: dV/dt = pi * 2r * dr/dt * h + pi * r^2 * dh/dt Now for the first part: dV/dt = pi * 2 * 8 * 2 * 12 + pi * 8^2 * -3 Second part: Increasing.
Why does it come out a negative number?
The answer is supposed to be 192 pi I don't get all the steps.

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Other answers:

The answer is 192pi. You must literally just do the calculation of what I wrote down, which gives 192pi.

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