Question

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?

Answer 1

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.

Answer 2

Why does it come out a negative number?

Answer 3

The answer is supposed to be 192 pi
I don't get all the steps.

Answer 4

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