Question

A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm. It is drawn out into a wire of diameter 1 mm. What will be the length of the wire so obtained?

Answer 1

Diameter of cylindrical metal =1 cm.

$\therefore$ Radius (r) $=\frac{1}{2}cm.$

Length (h)=11 cm.

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

$=\frac{22}{7}\times {\left(\frac{1}{2}\right)}^2\times 11c{m}^3=\frac{22}{7}\times \frac{1}{4}\times 11$

$=\frac{22}{7}\times \frac{11}{4}=\frac{121}{14}c{m}^3$

$\therefore$ Volume of wire $=\frac{121}{14}c{m}^3$

Diameter of wire =1 mm

$\therefore$ Radius $=\frac{1}{2}mm=0.5$ mm =0.05 cm.

Let length of wire =h

then $\pi r^{2}h=\frac{22}{7}\times (0.05{)}^2\times h$

$\Rightarrow \frac{22}{7}\times 0.0025\times h\frac{121}{14}$

$\Rightarrow h=\frac{121\times 7}{14\times 22\times 0.0025}$

$=\frac{121\times 7\times 10000}{14\times 22\times 25}=1100cm$

$\therefore$ Lenght of wire =11 m.