Question

If each edge of a cube is increased by $50\%$, then its surface area is increased to .

• A. $125\%$
• B. $150\%$
• C. $175\%$
• D. $110\%$

Answer 1

The correct option is A $125\%$

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

TSA of new cube = $6\times {\left(\frac{3a}{2}\right)}^2=6\times \frac{9a^2}{4}=2.25\times 6a^2$
= 2.25 $\times$ Total surface area of original cube
Increase in area = $[2.25\times 6a^2]-\left[6a^2\right]=(2.25-1)\times 6a^2=1.25\times 6a^2$
$\therefore$ Increase in area
$=1.25\times$ TSA of original cube
$\Rightarrow$ Increase $\%=125\%$