A copper wire $3 m m$ in diameter is wound about a cylinder whose length is $1.2 m$ and diameter $10 c m$ , so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of the copper wire to be $8.88$ gram per cm.

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Solution

We have
diameter of copper wire $d = 3 m m = \frac{3}{10} c m$

Height (length) of the cylinder $= 1.2 m = 120 c m$

Number of rounds taken by the wire to cover the curved surface of the cylinder $= \frac{h}{d} = \frac{120}{3 / 10} = 400$

Length of wire used in taking one round $= 2 π r = (2 \times 3.14 \times 5) c m = 31.4 c m$

Total length of wire used in converting the curved surface of the cylinder

$= (3.14 \times 400) c m = 12560 c m = 125.6 m$

Mass of the wire = Length $\times$ density $= 12560 \times 8.88 g r a m = 111532.8 g m = 111.533 k g$

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A copper wire 3mm in diameter is wound about a cylinder whose length is 1.2m and diameter 10cm, so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of the copper wire to be 8.88 gram per cm.

A copper wire $3 m m$ in diameter is wound about a cylinder whose length is $1.2 m$ and diameter $10 c m$ , so as to cover the curved surface of the cylinder. Find the length and mass of the wire, assuming the density of the copper wire to be $8.88$ gram per cm.