Question

If the edge of a cube is doubled, then the percentage increase in the volume of cube is :

• A. $100$%
• B. $500$%
• C. $300$%
• D. $700$%

Answer 1

The correct option is D $700$%

Let $a$ be the edge of cube.
We know, volume of the cube, $V=a^3$.

Given, the edge of the cube is doubled, i.e. edge $=2a$.
Then, Volume of new cube $=(2a{)}^3=8a^3$.

Therefore, Percentage increase $=\frac{\text{Change in volume}}{\text{Original volume}}\times 100$

$=\frac{8a^3-a^3}{a^3}\times 100=700$%.
$=\frac{7a^3}{a^3}\times 100=700$%.

Hence, option $D$ is correct.