Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let the edge is 'a' cm
New edge after increase $=a+50\%ofa=a+\frac{a}{2}=\frac{3a}{2}$
Total surface area of original cube $=6a^2$
TSA of new cube is

$6\times {\left(\frac{3a}{2}\right)}^2=6\times \frac{9a^2}{4}=\frac{27a^2}{2}$

So, the percentage increment from $6\times a^{2}to6\times \frac{9a^2}{4}$

$\Rightarrow$ percentage increment from $6a^{2}to\frac{27a^2}{2}$

$\because$ percentage increment from A to B is

$\Rightarrow \frac{(A-B)}{A}\times 100$

$\Rightarrow \frac{15a^2}{2}\times \frac{1}{6a^2}\times 100$

$\Rightarrow 125\%$ increament in the TSA