# 1. A copper wire, 3 mm in diameter, is wound about a cylinder whose length is 12 cm, and diameter 10 cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of copper to be 8.88 g per cm3.

A number of rounds are calculated by :

$=\ \frac{Height\ of\ cylinder }{Diameter\ of\ wire}$

$=\ \frac{12 }{0.3}\ =\ 40\ rounds$

Thus the length of wire in 40 rounds will be   $=\ 40\times 2\pi \times 5\ =\ 400 \pi\ cm\ =\ 12.57\ m$

And the volume of wire is: Area of cross-section  $\times$  Length of wire

$=\pi \times (0.15)^2\times 1257.14$

$=\ 88.89\ cm^3$

Hence the mass of wire is.$=\ 88.89\ \times 8.88\ =\ 789.41\ gm$

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