# Volume of Revolution: Frustum

• June 8th 2010, 12:03 PM
maxreality
Volume of Revolution: Frustum
My professor assigned a problem where we are to find the volume of a frustum revolved around the y-axis.

I'm not going to draw it out because the setup is standard. H = height, r = the top of the frustum, and R = the bottom of the frustum. We're to find it using both shells and disks.

I feel like I'm close. When I set it up, it basically looks like a rectangle with a triangle next to (think pyramid with the top cut off).

I divided it into two sections. Rectangle and Triangle. I integrated the rectangle which was easy. The problem I'm having is that I don't know the value for f(x). If he gave me an arbitrary function and asked me to do it then it wouldn't be an issue, but I don't have the function, and I'm stuck.

Any help is appreciated. Thanks in advance!
• June 8th 2010, 12:44 PM
Turiski
The rectangle has points at (0,0) (0,h) (r,0) (r,h)

The triangle has (r,0) (r,h) and (R,0).

If you are asking what the function is for the triangle in the formula, it is $y = \frac{h}{R-r}(x-R)$ because it is simply a line going from the top corner of the rectangle to the x-axis at R (I used point-slope). It will be a washer method, not disk because it is not adjacent to the axis of revolution