Wed March 09, 2011 By: Kumar Krishna

A solid cube chopped off at each of its 8 corners to create an equilateral triangle with three corners . the 24 corners are now joined to each other by diagonals .How many of these diagonals completely lie inside the cube explain clearly

Expert Reply
Wed March 09, 2011
Dear Student,
Following is the solution to your problem:-
The total number of diagonals that can be created from the 24 new corners
24C2 = 276, Including those that would be present on the faces of new shape formed.
Now since each of the face would have six vertices, it would have 6C2 diagonals on it faces i.e. 15 diagonals on each of the six faces, so the number of diagonals that would completely lie inside the would be =276 - 15*6 = 186
Team Topperlearning
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