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.