In geometry a cube is a three dimension solid having 6 square faces, 12 edges and 8 corners.

In cube for any cut we will get one more piece. Example :for 1 cut, we get 2 pieces ,for 2 cut ,we get 3 pieces.

Example: If 15 cuts are to be made on a cube, then what is the maximum possible number of identical pieces that can be formed ?
A) 204
B) 125
C) 216
D) None of these

Answer:C) 216

Explanation:
Here 5 cuts in each axis (X,Y ,Z ).So we get 6 pieces in each axis. Then total 6*6*6=216

Example:What is the minimum possible number of cuts required to form 729 identical pieces from cube ?
A) 24
B) 21
C) 27
D) None of these

Answer:A) 24

Explanation:

9*9*9=729.So in each axis we get 9 pieces and for this 8 cuts required in each axis. So possible number of cuts required
8+8+8=24

Example:What is the least number of cuts required to form exactly 100 identical pieces from a cube ?
A) 13
B) 14
C) 11
D) None of these

Answer:C) 11

Explanation:

100 lies between 4*4*4=64 and 5*5*5=125.So for 100 pieces we take 4*5*5=100.So total cuts required 3+4+4=11