Intersecting any CAD model with a box

For a give CAD model, I want to intersect the model with a rectangular block oriented in X,Y or Z that satisfies the following : 1-be as large as possible. 2-the percentage of empty volume inside the rectangle is minimum

For example, the box could be very large and intersects the model in large volume but still have large empty volume inside, a smaller box could be better if it intersects the model in smaller volume but have no or less empty spaces.

It's a multi objective optimization problem somehow maximize (the box volume) and minimize ( the volume of the box-the volume of the model inscribed in the box)

any recommendations?