# Thread: Help With Circular Cylinder Related Rates Problem

1. ## Help With Circular Cylinder Related Rates Problem

The diameter and height of a right circular cylinder are found at a certain instant to be 10 and 20 inches respectively. If the diameter is increasing at the rate of 1 inch per minute, what change in the height will keep the colume constant?

2. $V = Ah = \pi r^2h = \pi(d/2)^2h$

$\frac{dV}{dt} = \pi(d/2)\frac{dd}{dt}h + \pi(d/2)^2\frac{dh}{dt}$

D/2 = r = 5, h = 10

$\frac{dV}{dt} = 100\pi\frac{dd}{dt} + 25\pi\frac{dh}{dt}$

$\frac{dd}{dt} = 1$

$\frac{dV}{dt} = 100\pi + 25\pi\frac{dh}{dt}$

If volume is contant, dV/dt = 0

$0 = 100\pi + 25\pi\frac{dh}{dt}$

3. Thanks...it makes a lot more sense now