Question

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

(a) 3 times (b) 6 times

(c) 9 times (d) 27 times

Answer 1

In the first case, r and $h_1$ be the radius and

height of the cylindrical wire

$\therefore$ Volume = $\pi r^2{h}_1$

In second case, radius is decreased to one third

$\therefore$ Radius $=\frac{1}{3}r$

$\therefore$ Volume $=\pi {\left(\frac{1}{3}r\right)}^2{h}_2$

=$\frac{1}{9}\pi r^2{h}_2$ $\therefore$ Volume are equal

$\therefore \pi r^2{h}_1=\frac{1}{9}\pi r^2{h}_2$

$\Rightarrow h_1=\frac{1}{9}{h}_2\Rightarrow 9h_1=h_2$

$\therefore$ In second case is 9 times