# Thread: how to find the volume of a figure with this cross section

1. ## how to find the volume of a figure with this cross section

Hello, I need to figure out how to find the volume of this shape with a cross-sectional area that looks like this. This shape is rotated around a central axis to make a "ring".:

It is basically a triangle, but the hypotenuse is a small portion of a much larger circle instead of a straight line.

In order to find the volume of this "ring", I would first need to find the area of this shape, A. I would also need to find the center of gravity x-coordinate of the shape. Cgx I'll call it.

Once I have that information, I'd be able to find the volume of this ring. The volume would be:

Vr = 2*pi*A*(D+Cgx), where D is the distance from the center axis to the right leg of the shape.

I don't know how to find A or Cgx though...Can anyone help me with this please? Thanks a lot!

use the diagram below to help you determine the area and find the centroid.

Cheers!

3. Thanks a lot! I appreciate it.

4. Originally Posted by bkelly301
Thanks a lot! I appreciate it.

So did u get the right answer?

5. I'm not sure yet. I will be back at work on monday, and I will test it out first thing in the morning. To see how the problem applies to my job, I posted this same question in the geometry section, but it has more detail. I didn't get any replies there though. I'll keep you updated on Monday. Thanks again!

6. Yes, that worked! Thank you very much!