By what percent the volume of a cube increases if the length of each edge was increased by 50%

Solution (By Examveda Team)

Let original edge = a
Then, original volume = a³
New edge :
$$\eqalign{ & = \frac{{150}}{{100}}a \cr & = \frac{{3a}}{2} \cr} $$
New volume :
$$\eqalign{ & = {\left( {\frac{{3a}}{2}} \right)^3} \cr & = \frac{{27{a^3}}}{8} \cr} $$
Increase in volume :
$$\eqalign{ & = \left( {\frac{{27{a^3}}}{8} - {a^3}} \right) \cr & = \frac{{19{a^3}}}{8} \cr} $$
∴ Increase % :
$$\eqalign{ & = \left( {\frac{{19{a^3}}}{8} \times \frac{1}{{{a^3}}} \times 100} \right)\% \cr & = 237.5\% \cr} $$