Question

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.

Answer 1

$diameter \: of \: wire = 3 \: mm = 0.3 \: cm$
$number \: of \: turns \: of \: wire \: on \: \\ cylinder = \frac{length \: of \: cylinder}{diameter \: of \: wire} \\ = \frac{12}{0.3} = 40$
$length \: of \: one \: turn \: of \: wire = \\ perimeter \: of \: cylinder = \pi \times 10$
$total \: length \: of \: wire = 40 \times (10\pi) \\ = 400\pi$
$volume \: of \: wire = \\ \frac{\pi}{4} \times ( {0.3}^{2} ) \times 400\pi = 9 {\pi}^{2} \: {cm}^{3}$
$mass \: of \: wire = 8.88 \times 9 {\pi}^{2} \\ = 787.97 \: g$

Answer 2

Answer:

Check your answer please