Question

The radius of a wire is decreased to one-third. If volume remains the same the length will become

• A. $1$ time
• B. $3$ times
• C. $6$ times
• D. $9$ times

Answer 1

The correct option is D $9$ times

Wire is in the shape of a cylinder.
Let the radius of the original cylinder $=r$ cm and height $=h$ cm
Original volume $=\pi r^{2}h$

New Radius after decrease $=\frac{r}{3}$


Let the new height be H.

Given, $\pi r^{2}h=\pi {\left(\frac{r}{3}\right)}^{2}H$
$H=9h$
Hence, the height becomes 9 times.