Question

If each edge of a cube is increased by $25$ %, then the percentage increase in its surface area is

• A. $25$%
• B. $48.75$ %
• C. $50$ %
• D. $56.25$ %

Answer 1

Answer: (D)

$56.25$ %

Let original edge be 'a' ,Surface area = 6a${}^2$
New edge $=\frac{125}{100}a=\frac{5a}{4}$
New surface area
$=6\times {\left(\frac{5a}{4}\right)}^2=\frac{75a^2}{8}$
Increase in surface area
$=\left(\frac{75a^2}{8}-6a^2\right)=\frac{27a^2}{8}$
$\therefore$ increase %
$=\left(\frac{27a^2}{8}\times \frac{1}{6a^2}\times 100\right)\%$
$=56.25$%