Given: Edge of a cube is increased by 50%

Let ‘a’ be the Edge of the cube

Area of the cube is : 6l² (where ‘l’ is the edge of a cube)

Let A₁ be the initial surface area of the cube.

∴ A₁ = 6a²

Now,

50% of the edge is: a × =

∴ Edge = a + after increasing edge by 50%

That is edge of the cube after increasing it by 50% is

Let A₂ be the surface area of the cube after increasing the edge by 50%

∴ A₂= 6 × ()² = × 6a²

Here increase in area = A₂ –A₁

⇒ increase in area = × 6a² – 6a² = × 6a²

Now, increase in percentage is:

Increase in % = × 100 = × 100 = 125%

∴ If each edge of a cube is increased by 50%, then the percentage increase in the surface area is 125%