Each edge of a cube is increased by 50%.
Question:

Each edge of a cube is increased by 50%. Find the percentage increase in the surface area of the cube.

Solution:

Let the initial edge of the cube be a units.

∴ Initial surface area of the cube = 6a2 square units

New edge of the cube $=a+50 \%$ of $a=a+\frac{50}{100} a=1.5 a$ units

$\therefore$ New surface of the cube $=6(1.5 a)^{2}=13.5 a^{2}$ square units

Increase in surface area of the cube $=13.5 a^{2}-6 a^{2}=7.5 a^{2}$ square units

∴ Percentage increase in the surface area of the cube

$=\frac{\text { Increase in surface area of the cube }}{\text { Initial surface area of the cube }} \times 100 \%$

$=\frac{7.5 a^{2}}{6 a^{2}} \times 100 \%$

$=125 \%$

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