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!