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

The correct option is 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 be the new length of the wire, then by hypothesis,
$\pi r^{2}h=\pi {\left(\frac{r}{2}\right)}^2{h}^{\prime }=\frac{\pi r^{2}h}{4}$
$\therefore h^{\prime }=4h=4$ times h.