Question

If each edge of a cube is increased by $50\%$, the percentage increase in its surface area is

• A. 50%
• B. 75%
• C. 100%
• D. 125%

Answer 1

The correct option is D

125%

Let in first case, edge of a cube = a

$\text{Then surface area}=6a^2$

$\text{In second case, increase in side}=50\%$

$\therefore Side=a\times \frac{100+50}{100}$

$=a\times \frac{150}{100}=\frac{3}{2}a$

$\therefore \text{Surface area}=6{\left(\frac{3}{2}a\right)}^2$

$=6\times \frac{9}{4}{a}^2=\frac{27}{2}{a}^2$

$\text{Increase in area}=\frac{27}{2}{a}^2-6a^2$

$=\frac{15}{2}{a}^2$

$\therefore \text{Percent increase}=\frac{15a^2}{2}\times \frac{100}{6a^2}$

$=125\%$