# rate of change

• Aug 22nd 2007, 09:46 AM
Samantha
rate of change
A machine is rolling metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128 $\pi$ cubic inches. At what rate is the length H changing when the radius r is 2.5 inches? $[Hint: V = \pi r^2 h]$
• Aug 22nd 2007, 10:32 AM
TKHunny
Quote:

Originally Posted by Samantha
A machine is rolling metal cylinder under pressure. The radius of the cylinder is decreasing at a constant rate of 0.05 inches per second and the volume V is 128 $\pi$ cubic inches. At what rate is the length H changing when the radius r is 2.5 inches? $[Hint: V = \pi r^2 h]$

Note: It would help if you could post in a less general category and profide a more descriptive title. It might give a clue as to your level or what class you are in or what tools should be used.

In this case, it's a nice differential calculus problem. If you're in a different class, that will be a problem.

r and h are functions of time.
V is constant, so dV = 0
dr is given as -0.05"/sec
Find dh when r = 2.5"

Complete derivative:

$V = \pi r^2 h$

$dV = \pi \left(r^{2}\frac{dh}{dt} + h*\left(2r\frac{dr}{dt}\right)\right)$

dV is known.
r is given.
dh/dt is what we need. We'll have to solve for it after everything else is found.
h - You will have to solve for this from the Hint.
dr/dt is given.
Substitute and solve.