Question

Each edge of a cube is increased by $20\%.$ What is the percentage increase in the volume of the cube?

Answer 1

Let the initial edge of the cube be $l.$ Then, its volume is $V=l^3$.

New edge after being increased $20\%=L=l+l\times \frac{20}{100}=l+\frac{l}{5}=\frac{6l}{5}$

$\therefore$ New Volume, $V^{\prime }=L^3=[\frac{6l}{5}{]}^3=\frac{216}{125}{l}^3$

Increase in volume $=△V=V^{\prime }-V=\frac{216}{125}{l}^3-l^3=\frac{216-125}{125}{l}^3=\frac{91}{125}{l}^3$

$\therefore$ Percentage increase in the volume of the cube $=\frac{△V\times 100}{V}=\frac{91l^3\times 100}{125\times l^3}=\frac{9100}{125}=72.8\%$