As each of a group of business people arrives at a meeting, each shakes hands with all the other people present.
(A) Use mathematical induction to show that if n people come to the meeting then [n(n−1)]/2 handshakes occur.

Edge length of the side of a cube = 5 inches
Then
Volume of the cube = (side)^3
                                = (5)^3
                                 = 125 inches ^3
So the volume of the actual cube is 125 inches^3
Now after the side lengths are triple, then
New edge length of each side = 3 * 5 inches
                                                = 15 inches
Then
New volume of the cube = (New side)^3
                                        = (15)^3
                                         = 3375 inches^3
Then the volume of the new  cube is 3375 inches^3
So
The number of times the volume of the new cube is greater = 3375/125
                                                                                                 = 27
So the volume of the new cube is 27 times greater than the old cube.