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?
Solution:
Diameter of the given wire $=1 \mathrm{~cm}$
Radius $=0.5 \mathrm{~cm}$
Length $=11 \mathrm{~cm}$
Now, volume $=\pi r^{2} \mathrm{~h}=\frac{22}{7} \times 0.5 \times 0.5 \times 11=8.643 \mathrm{~cm}^{3}$
The volumes of the two cylinders would be the same.
Now, diameter of the new wire $=1 \mathrm{~mm}=0.1 \mathrm{~cm}$
Radius $=0.05 \mathrm{~cm}$
$\therefore$ New length $=\frac{\text { volume }}{\pi \mathrm{r}^{2}}=\frac{8.643 \times 7}{22 \times 0.05 \times 0.05}=1100.02 \mathrm{~cm} \cong 11 \mathrm{~m}$