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 side of the cube be $x$.

Then its total surface area $=6x^2$.
If each side is increased to $\frac{3}{2}x$
Total surface area $=6\times \frac{3x}{2}\times \frac{3x}{2}=\frac{27x^2}{2}$
$\therefore$ Increase $=\frac{27x^2}{2}-6x^2=\frac{15x^2}{2}$
$\therefore$ $\%$ increase $=\frac{15x^2}{2}\times \frac{100}{6x^2}=125$