Create a radial (shadowing) extrusion

I'm looking for a way to do the equivalent of an "up to next" extrusion, but starting from a point rather than a plane.  For some reason I can't insert my image of what I want to do so I'm attaching it instead.  Basically the goal is to illustrate a shadow (of a more complicated object) from a point source.  Ideally I want to end up with the negative of this, but either way, I need to figure out a way to get there.  This drawing was actually done in reverse, creating a sphere, extruding a cut with a large negative draft so it came to a point at the center, reducing the length of the extrusion, then converting the square surface and making the cube.  However, that's only to illustrate the concept.  What I want is the ability to create the cube (or any shape object) and then create the radial extrusion that would stop when it hits a surface.  That would leave a negative image of the shadow of the object.  Alternately if there was a direct way to create the shadow, that would work too.  It's almost like a mold part, but the separation line and draft would need to be automatic based on the desired point.   

Any suggestions on how to bend Solidworks to my will here would be greatly appreciated.  Note that I CAN use Photoview to project a "real" shadow on the surface of a hemisphere, but that becomes a flat circle and can't be manipulated.  It also requires removal of other objects that I want in the drawing but don't want to have cast a shadow.

Thanks,

Michael

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