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/$${cm}^3$. (Use $\pi =3.14$)

Answer 1

It is assumed that one round of copper wire will cover $3mm$ or $0.3cm$ height of cylinder.

Number of rounds $=\frac{\text{Height of the cylinder}}{\text{Diameter of the wire}}$

$=\frac{12}{0.3}$

$=40rounds$

Now, the length of the wire required in one round $=$ Circumference of the base of the cylinder.

Diameter of the cylinder $=10cm$, so the radius $=5cm$.

Therefore circumference $=2\pi r=2\pi \times 5=10\pi$

Length of wire required in one round $=10\pi$

Length of wire required in $40$ rounds $=10\pi \times 40$

$=400\times 3.14$

$\therefore$ Length of the wire $=1257.14cm$

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

Volume of wire = Area of cross section of wire $\times$ length of the wire

$=\pi r^2\times 1257.14$

$=3.14\times (0.15{)}^2\times 1257.14$

$\therefore$ Volume of the wire $=88.898c{m}^3$

Mass $=$ Density $\times$ Volume

$=8.88\times 88.898$

$\therefore$ Mass $=789.41gm$