Multiple choice

A wire having diameter 3 mm.is wound about a cylinder whose length is $12 cm$ and diameter $10cm$, so as to cover the curved surface of the cylinder. Find the length and mass of the wire. Assume that the density of the material of the wire is $8.88$ gm per ${cm}^{3}$ ?

  1. $1256 cm, 788 g$
  2. $1256,800 g$
  3. $1200, 788 g$
  4. $1156 cm, 769 g$
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A Correct answer
Explanation

The number of turns is 12 cm / 0.3 cm = 40 turns. Each turn has a circumference of pi * 10 cm. Total length = 40 * 10 * pi = 400 * 3.14 = 1256 cm. Volume = area * length = pi * (0.15)^2 * 1256 = 88.8 cm^3. Mass = 88.8 * 8.88 = 788 g.

AI explanation

To cover the 12 cm cylinder height using wire of 3 mm thickness, the number of turns required is 12 cm divided by 0.3 cm, which equals 40 turns. In one turn, the length of wire needed equals the circumference of the cylinder, computed using the circumference formula as pi * 10 cm. Multiplying the 40 turns by 31.4 cm gives a total wire length of 1256 cm. We then find the volume of the wire using the cylinder volume formula V = pi * (0.15)^2 * 1256, which equals about 88.736 cm^3. Finally, we multiply this volume by the given density of 8.88 g/cm^3 to get a mass of approximately 788 g.

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