Tricky Rates of Change Question

"Water is being poured into a conical vessel of semi vertical angle of 30 degrees at the rate of 100Pi cm cubed per minute. find the rate at which the depth pf water is increasing when the water is 5cm deep."


I can't really seem to get my head around this question.
As far as I can make out it involves a little bit of trigonometery which I'm terrible at. The only thing I can make out so far is that I'm looking for dV/dT. :o

All help really appreciated!
The question is worth quit a bit of my exam.

Welcome to the forums.

With problems like this, it really helps to:

1. Draw a picture and label pertinent information
2. Write what you know in mathematical terms
3. Write what you are looking for in mathematical terms
4. Use the information in the problem to figure out how to get what you need

For 1, I presume you have or can find the formula for the volume of a cone - probably in terms of radius r and depth h.

For 2, you are given the amount of water that is being poured into the cone. What is that in derivative terms?

For 3, what are you really looking for? Is it really dV/dt?

Ultimately what you need to do is develop an expression for V = f(h), where h is depth. You can do that using the forumula for volume, one of the trig functions and the cone angle that is given. Just draw it out, it's very straightforward.

Once you are clear on what you have (in derivative terms) and what you want (in derivative terms), you can use the information to get what you want.

Hint: chain rule will be useful