Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

Answer:

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

Now,

Percentage increase in the surface area = ((15/2)x2 / 6x2) x 100

= 15/12 x 100

= 125%

Therefore, the percentage increase in the surface area of a cube is 125.

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