# Calculating Volume With Center of Mass

1. Mar 7, 2013

### iRaid

I remember seeing a way to do this, can someone link me to some relevant material or post a proof and equation?

Thanks

2. Mar 7, 2013

### SteamKing

Staff Emeritus
Your request is a little ambiguous. Do you want to calculate the centroid of a volume or do you want to calculate the center of gravity of a mass? The two may not necessarily be the same.

3. Mar 7, 2013

### iRaid

I'm sorry. I mean: given a function, f(x) and rotating it around the x-axis. Can you find the volume of this function using the centroid/center of mass (I was told these are the same...)?

4. Mar 7, 2013

### SteamKing

Staff Emeritus
You want to look up the Theorems of Pappus.

5. Mar 8, 2013

### iRaid

So it is:
$$2\pi A\bar{x}$$
Where A is the area between 2 curves and x bar is the center of mass.

6. Mar 8, 2013

### SteamKing

Staff Emeritus
x-bar is the centroid of the area being revolved, measured with respect to the axis of revolution.