- #1

starstruck_

- 185

- 8

## Homework Statement

((I cannot, for the love of life, understand related rates, so please bear with me. Thank you! ))

A cylindrical tank with radius 5m is being filled with water at a rate of 3m

^{3}/min. How fast is the height of the water increasing?

I'm having trouble interpreting this question - actually, most related rates questions, having trouble differentiating between what I would call the volume and what not.

## Homework Equations

v= (pi)r

^{2}h

## The Attempt at a Solution

So, I'm going to say that I know the rate of change of the volume - which means I need to get the height in terms of the volume?

since v= (pi)r

^{2}h

h= v/((pi)r

^{2})

h' = (dy/dx [v]((pi)r

^{2}) - dy/dx[(pi)r

^{2}](v))/((pi)

^{2}r

^{4})

h' = (3(2pir^2) - 2pirv)/ ((pi)

^{2}r

^{4})I'm pretty sure this is wrong since I ended up with a "v" in my numerator which I don't know the value of.

How would I go about solving this?