Question

The percentage increase in the surface area of a cube, when each side is increased to $\frac{3}{2}$ times the original length is

• A. $225$
• B. $200$
• C. $175$
• D. $125$

Answer 1

The correct option is D $125$

Let, edge of a cube $=x$

Then, surface area of a cube$s_1=6x^2$

When each side is increased to $\frac{3}{2}$ times of original length then surface area ,

$s_2=6.{\left(\frac{3}{2}x\right)}^{2}c{m}^2$

$=13.5x^{2}c{m}^3$

Now, percentage increase in surface area of a cube,

$=\frac{13.5x^2-6x^2}{6x^2}\times 100$

$=125$ percent

Hence, this is the answer.