# Nailing down related rates questions

## Main Question or Discussion Point

Hi,

I am terrible when it comes to doing these questions. I was wondering if you guys have any tips on how to do these questions. Like for example, just say there's a question like the following:

Water is poured into a reservoir in teh shape of a cone 6ft. tall with a radius of 4ft. If water level is rising at 0.5ft/s. How fast is the water being poured at the instant the depth is 2ft?

When I see that kind of question, I am clueless on how to even start it out. Is there a trick to doing them? I just don't understand the concept literally.

Any hlep would be great thanks.

## Answers and Replies

dextercioby
Homework Helper
HINT:
$$V(r(t),h(t))=\frac{\pi r^{2}(t)h(t)}{3}$$

U're interested in the quantity
$$\frac{dV(r(t),h(t))}{dt}|_{h=2ft}$$

Daniel.

Gokul43201
Staff Emeritus
Gold Member
The trick is to first transcribe all the given data into equations and write them down. Then write down in the same form, what the question (the desired quantity) translates to.

Do this for the given example and then you'll see how the given data can be related to the required quantity.

Hurkyl
Staff Emeritus