Question

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

Options

• 50%

• 75%

• 100%

• 125%

Answer 1

 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 

${\displaystyle =\frac{150\text{a}}{100}}$

${\displaystyle =\frac{3\text{a}}{2}}$

Hence, new surface area ${\displaystyle =6 \times {\left(\frac{3\text{a}}{2}\right)}^2}$

${\displaystyle =\frac{27a^2}{2}}$

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

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

% increasein surface area ${\displaystyle =(\frac{{\text{15a}}^2}{2}\times \frac{1}{6{\text{a}}^2\times 100})\%}$

=125 %