Question

A copper wire, $3mm$ in diameter, is wound about a cylinder whose length is $12cm$, 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 copper to be $8.88g$ per $c{m}^3$.

Answer 1

From the figure we can observed that $1$ round of wire will cover $3$ mm height of cylinder.
Number of rounds = $\frac{Heightofcylinder}{Diameterofwire}$
$=\frac{12}{0.3}$$=40$ rounds.

Length of wire required in $1$ round = Circumference of base of cylinder
$=2\pi r=2\pi 5=10\pi$

Length of wire in $40$ rounds $=40\times 10\pi$
$=\frac{400\times 22}{7}=\frac{8800}{7}=1257.14$ cm
$=12.57$ m

Radius of wire = $\frac{0.3}{2}=0.15$ cm.

Volume of wire = Area of cross-section of wire x Length of wire
$=\pi (0.15{)}^2\times 1257.14$
$=88.898c{m}^3$

Mass = Volume x Density
$=88.898\times 8.88$
$=789.41$ gm