Question

If the edge of a cube increases by $10$%, then find the percentage increase in its volume.

• A. $20$%
• B. $30$%
• C. $66.6$%
• D. $33.1$%

Answer 1

The correct option is D $33.1$%

We know, Volume of cube $={\left(side\right)}^3$.
If $a$ s the original side, then Volume of cube $=a^3$.
When the side of the cube increases by $10$ %, new side $=1.1\times a$.
Then, New Volume $={\left(1.1a\right)}^3=1.331a^3$.
Therefore, % Increase in volume $=\frac{\text{New Volume}-\text{Old Volume}}{\text{Old Volume}}\times 100$

$=\frac{1.331a^3-a^3}{a^3}\times 100$

$=0.331\times 100=33.1\%$.

Hence, option $D$ is correct.