Thread: Finding the area of this shape - almost like a triangle, but the hypotenuse is round

Here's my problem:

I'm trying to figure out how to calculate the volume of this figure:



(Please excuse the crappy drawing).

Anyway, this is a cross section of a "ring". I usually deal with rings with rectangular cross-sections, in which case it is simple to figure out the volume:

volume of "rectangular cross-sectioned ring":

pi/4*(OD^2 - ID^2) * height = volume of ring

Simple.

But for this figure, in order to calculate the total volume, I need 3 volumes:

VLOD - VID - 2*VR = Total volume

Where,

VLOD = pi/4*LOD^2*H
VID = pi/4*ID^2*H
VR = what I don't know how to figure out???

The radius is actually a small portion of a much larger circle, in which I know the coordinates of the center. I'm thinking I need to find the center of gravity of this shape in order to find the area, but I've been looking and looking and looking, and I can't seem to figure this one out.

If anyone can help, I'd greatly appreciate it. Thanks a lot!

Originally Posted by bkelly301

Here's my problem:

I'm trying to figure out how to calculate the volume of this figure:



(Please excuse the crappy drawing).

Anyway, this is a cross section of a "ring". I usually deal with rings with rectangular cross-sections, in which case it is simple to figure out the volume:

volume of "rectangular cross-sectioned ring":

pi/4*(OD^2 - ID^2) * height = volume of ring

Simple.

But for this figure, in order to calculate the total volume, I need 3 volumes:

VLOD - VID - 2*VR = Total volume

Where,

VLOD = pi/4*LOD^2*H
VID = pi/4*ID^2*H
VR = what I don't know how to figure out???

The radius is actually a small portion of a much larger circle, in which I know the coordinates of the center. I'm thinking I need to find the center of gravity of this shape in order to find the area, but I've been looking and looking and looking, and I can't seem to figure this one out.

If anyone can help, I'd greatly appreciate it. Thanks a lot!

The bulk of the volume is in the ring = OD^2 pi/4 - ID^2 pi /4)x H . The torus part must be subtracted. Take the half circle of torus area and multiply by 2pi (OD /2 -r /2) Where r is the radius of the torus. Comments?



bjh