Question

If the length of each edge of a cube increases by 20%, then the volume of the cube increases by _________.

Answer 1

Let the length of each edge of the original cube be a units.

∴ Volume of the original cube = a³

If the length of each edge of a cube increases by 20%, then

Length of each edge of new cube = a + 20% of a = $a+\frac{20}{100}a=a+\frac{1}{5}a=\frac{6a}{5}$

∴ Volume of the new cube $={\left(\frac{6a}{5}\right)}^3=\frac{216a^3}{125}$

Percent increase in volume of cube

$=\frac{\mathrm{Increase}\mathrm{in}\mathrm{volume}\mathrm{of}\mathrm{cube}}{\mathrm{Original}\mathrm{volume}\mathrm{of}\mathrm{cube}}\times 100\%$

$=\frac{{\displaystyle \frac{216}{125}}{a}^3-a^3}{a^3}\times 100\%$

$=\frac{216-125}{125}\times 100\%$

$=\frac{91}{125}\times 100\%$

$=72.8\%$

Thus, the volume of the cube increases by 72.8%.

If the length of each edge of a cube increases by 20%, then the volume of the cube increases by ___72.8%___.