- #1

opus

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## Homework Statement

Evening all. I have a related rates problem that I haven't come across which doesn't seem to involve time which is usually the independent variable that we take the derivative with respect to. It has thrown me for a loop.

Find the change in the volume of a right cylinder cone with a height of 2 if the radius r changes from 0.5 to 0.55.

## Homework Equations

##V = \frac{1}{3}πr^2h##

## The Attempt at a Solution

The set up is where I'm not doing too well. Normally, if the related rates problem had time as an independent variable, I would do as such:

1) Find an equation that relates the variables to each other.

2) Find an equation that shows the rate of change with respect to the independent variable (time usually).

3) Take the derivative of both sides of the equation relating the variables to each other with respect to the independent variable. I would now have an equation that relates the rates of change of everything.

4) Plug in the given rate of change, and solve for the other rate of change.

In this case, as far as I've gotten is to say that I want the change in volume when the change in radius is 0.05 which is given in the question. The change in volume seems to need to be written as ##\frac{dV}{dr}##, as we want the change in volume with respect to the radius. But as for writing the change in radius, it doesn't make sense to write ##\frac{dr}{dr}##.

Another thing I did is to get the equation in terms of just radius so I'm working with less variables:

##V = \frac{1}{3}πr^2\left(\frac{2r}{r}\right)## but I don't think this is being much help.

As you can see, I am a mess with this one, so any pointers would be greatly appreciated!