Let x be the edge of a cube.
Surface area of the cube having edge x = 6x2 ………..(1)
As given, a new edge after increasing the existing edge by 50%, we get
The new edge = x + 50 x /100
The new edge = = 3x/2
Surface area of the cube having edge 3x/2 = 6 x (3x/2)2= (27/2)x2……..(2)
Subtract equation (1) from (2) to find the increase in the Surface Area:
Increase in the Surface Area = (27/2)x2 – 6x2
Increase in the Surface Area = = (15/2)x2
Percentage increase in the surface area = ((15/2)x2 / 6x2) x 100
= 15/12 x 100
Therefore, the percentage increase in the surface area of a cube is 125.