Question

If each edge of a cube is increased by 50%, the percentage increase in the surface area is
(a) 50%
(b) 75%
(c) 100%
(d) 125%

Answer 1

(d) 125%
Let the original edge of the cube be a units.
Then, the original surface area of the cube = 6a² units

New edge of the cube = 150% of a
$$\begin{gathered} =\frac{150a}{100} \\ =\frac{3a}{2} \end{gathered}$$
Hence, new surface area$=6\times {\left(\frac{3a}{2}\right)}^2$
$=\frac{27a^2}{2}$
Increase in area$=\left({\displaystyle \frac{27a^2}{2}}-6a^2\right)$
$=\frac{15a^2}{2}$
% increase in surface area$=\left({\displaystyle \frac{15a^2}{2}}\times {\displaystyle \frac{1}{6a^2}}\times 100\right)\%$
= 125 %