Question

Length of each side of a cube is increased by 25%. Then the percentage increase in volume will be ___.

Answer 1

Let length of each side of cube be 'a'

Then, volume = $a^3$

New length = a + 25% of a

$=a+\frac{25\times a}{100}=\frac{5a}{4}$

$\text{New volume}={\left(\frac{5a}{4}\right)}^3=\frac{125}{64}{a}^3\text{Increase in volume}$

$=\frac{125}{64}{a}^3-a^3$

$=\frac{(125-64)a^3}{64}$

$=\frac{61}{64}{a}^3$

$\%\text{Increase in volume}=(\frac{\text{Increase in volume}}{\text{Initial volume}}\times 100\%)$

$=\frac{\frac{61}{64}{a}^3}{a^3}\times 100\%$

$=\frac{61}{64}\times 100\%=95.31\%$