Related Rates Problem

Question

The volume of a cylinder of height 12 inches and radius r inches is given by the formula V = 12pir ^2

if the expression for dV/dt = 24pir dr/dt

And suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.8 inches? Use at least 5 decimal places in your answer.

Explain how to find the answer in cubic inches per second.

Answer 1

1. V = 12 pi r^2
2. dV/dt = 24pir dr/dt
3. radius is expanding at a rate of 0.6 inches per second => dr/dt = 0.6 in/sec
4. dV/dt = 24 * pi *2.8* 0.6 = 126.66902 in^3/sec