The following question comes from the subject test:
A tetrahedron was cut from the corner of a cube, with three of its vertices at the midpoints of three edges of the cube. If tetrahedrons of the same size are cut from the remaining seven corners of the cube, how many faces will the resulting solid have?
Thank you and big hugs!
The image you tried to attach didn’t work, unfortunately, so maybe you can upload it in the comments under this post for the benefit of everyone else.
The thing to recognize, though, is that what’s being described is basically chopping off a corner of the cube—the figure makes that more clear than the description. When you chop off a corner of a cube, you add a face to the solid. A cube has 6 faces, but a cube with a corner chopped off has 7 faces.
A cube has 8 corners in all. If you chop them all off, you add 8 faces to the solid. Add those 8 to the 6 faces the cube already had, and your new solid has 14 faces.