Question

If each edge of a cube is increased by 50%, then the percentage increase in its surface area is.​

Answer 1

Answer:

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

Step-by-step explanation:

Let x be the edge of a cube.

Surface area of the cube having edge $x = 6x^2$ (1)

As given, a new edge after increasing the existing edge by 50%, we get

The new edge

 $x + \frac{50x}{100} \\= x+\frac{x}{2} \\=\frac{3x}{2}$

 

Surface area of the cube having edge $= 6 x (3x/2)^2= (27/2)x^2$ (2)

Subtract equation (1) from (2) to find the increase in the Surface Area:

Increase in the Surface Area $= (27/2)x^2 – 6x^2$

Increase in the Surface Area $= (15/2)x^2$

Now,

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

= 15/12 x 100

= 125%

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