The radius of a right circular cylinder is increasing at the rate of 6 in./s, while the height is decreasing at the rateof 3 in./s. at what rate is the volume of the cylinder changing when the radius is 5 in. and the height is 11 in.?

The rate at which the volume of the cylinder changes is 480πin³/s

The formula for calculating the volume of a cylinder is expressed as:

The change with respect to time is expressed as:

Given the following parameters:

Substitute the given values into the formula:

Hence the rate at which the volume of the cylinder changes is 480πin³/s

Learn more on the volume of cylinder here: link

The volume of a cylinder with radius and height is

Differentiate both sides with respect to time:

We're given that

so that at the point when and , the volume is undergoing a total change of

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!

43

step-by-step explanation: