The length of each edge of a cube is increased by 50%. The percentage increase in the surface area is:

Correct option is D

​Given:

Edge length increased by 50%

Formula Used:

$$\text{Percentage increase in surface area} = \left(\frac{\text{New surface area} - \text{Original surface area}}{\text{Original surface area}}\right) \times 100$$​​

Surface area of a cube: 6a²

Solution:

Original surface area: 6a² 

Increase length by 50%

New edge length: 1.5a.

New surface area:

$$6(1.5a)^2 = 6 \times 2.25a^2 = 13.5a^2$$ 

Increase in surface area:

$$13.5a^2 - 6a^2 = 7.5a^2$$​​

Percentage increase:

$$\left(\frac{7.5a^2}{6a^2}\right) \times 100 = 125\%$$