# Math Help - Related Rates.. HELP!

1. ## Related Rates.. HELP!

Water is draining at the rate of 48Pi ft^3/min from the vertex at the bottom of a conical tank whose radius at its base is 20 feet and whose height is 60 feet.(volume of a cone is V= 1/3Pir^2h)

A. Find an expression for the volume of water in the tank in terms of its radius at the surface of the water. (hint:use similar triangles)

What the hell do I do? There's similar triangles in the picture given, but what the heck am I suppose to do?? Take the derivative???

B.At what rate is the radius of the water in the tank shrinking when the radius is 16 feet?

C.How fast is the height of the water in the tank dropping at the instant that the radius is 16 feet?

2. $V = \frac{\pi}{3}r^2 h$

using the similar triangles ...

$\frac{r}{h} = \frac{20}{60}$

$h = 3r$

$V = \pi r^3$

proceed.

3. I got .0625 for B, is it correct?

How am I suppose to do C??

4. Originally Posted by Reefer
I got .0625 for B, is it correct?
$\frac{dr}{dt} = -\frac{1}{16}$ ft/min

Originally Posted by Reefer
How am I suppose to do C??
$\frac{d}{dt}[h = 3r]$