Math Help - How can I find the Volume of a frustum with elliptical top

1. How can I find the Volume of a frustum with elliptical top

Hi, I had an image like this on a test. I know it’s a version of a frustum only with an elliptical top making a 45 degree angle with the floor. I’ve been browsing search engines for hours with no clear definition of the image or finding the volume. The image is posted below.

My questions:

Does this image have a specific name?
Is there a formula that calculates the surface area?
Is there a formula that calculates the volume?

Thanks for any help with this,

Coopsterdude

2. As far as I know, this solid is simply a truncated cone ... technically not a frustrum since the plane of the base and the slicing plane are not parallel.

Someone has probably worked out the general formulae for the volume and surface area, although I have not seen them listed in any general resource.

Given the 45 degree angle for the slicing plane, it would not be an impossible task to calculate the volume or surface area ... but to make the calculation easier would require techniques from calculus.