Question

If each edge of a cube of volume $V$ is halved, then the volume of the new cube is __________.

• A. $\frac{V}{8}$
• B. $\frac{V}{4}$
• C. $\frac{V}{2}$
• D. $8V$

Answer 1

The correct option is A $\frac{V}{8}$

Let $a$ be the edge of original cube and $V$ be its volume. Volume of cube is given by:
$V=a^3$

Given, edge of new cube is:
$a^{\prime }=\frac{a}{2}$

$\therefore$ Volume of the new cube is:
$V^{\prime }={\left(\frac{a}{2}\right)}^3$
$V^{\prime }=\frac{a^3}{8}$
$V^{\prime }=\frac{V}{8}$