Question

The radius of a piece of wire is decreased to one-half. If volume remains the same, then its length will increase

• A. $2$ times
• B. $3$ times
• C. $4$ times
• D. $5$ times

Answer 1

Answer: (C)

$4$ times

Let $r$ and $h$ be the radius and length of a wire.
$\therefore$ volume of wire $=\pi r^{2}h$
New radius of wire $=\frac{r}{2}$
If $h^{\prime }$ be the new length of the wire, then by hypothesis,
$\pi r^{2}h=\pi {\left(\frac{r}{2}\right)}^2{h}^{\prime }=\frac{\pi r^2{h}^{\prime }}{4}$
$\therefore h^{\prime }=4h$
$\therefore h^{\prime }=4$ times $h$