A copper rod of diameter 1 cm and length

Question:

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Solution:

The radius of the copper rod is 0.5 cm and length is 8 cm. Therefore, the volume of the copper rod is

$V=\pi \times(0.5)^{2} \times 8 \mathrm{~cm}^{3}$

Let the radius of the wire is r cm. The length of the wire is 18 m=1800 cm. Therefore, the volume of the wire is

$V_{1}=\pi \times(r)^{2} \times 1800 \mathrm{~cm}^{3}$

Since, the volume of the copper rod is equal to the volume of the wire; we have

$V_{1}=V$

$\Rightarrow \pi r^{2} \times 1800=\pi \times(0.5)^{2} \times 8$

$\Rightarrow r^{2}=\frac{0.25 \times 8}{1800}=\frac{1}{900}$

$\Rightarrow r=\frac{1}{30}=0.033 \mathrm{~cm}$

So, thickness $=0.33 \times 2=0.66 \mathrm{~mm}$

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