The radius of a right circular cylinder is increasing at the rate of 7 in./sec, while the height is decreasing at the rate of 6 in./sec. At what rate is the volume of the cylinder changing when the radius is 20 in. and the height is 16 in.

Step-by-step explanation:

Given:

Rate of change of radius of cylinder:

(This is increasing rate so positive)

Rate of change of height of cylinder:

(This is decreasing rate so negative)

To find:

Rate of change of volume when r = 20 inches and h = 16 inches.

Solution:

First of all, let us have a look at the formula for Volume:

Differentiating it w.r.to 't':

Let us have a look at the formula:

Applying the two formula for the above differentiation:

Now, putting the values:

So, the answer is:

b

step-by-step explanation: