A piece of ductile metal is in the form of a cylinder of diameter 1 cm and length 11 cm.

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 $=\frac{\text { volume }}{\pi \mathrm{r}^{2}}=\frac{8.643 \times 7}{22 \times 0.05 \times 0.05}=1100.02 \mathrm{~cm} \cong 11 \mathrm{~m}$

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