Question

A copper wire of diameter 6 mm is evely wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of copper be 8.8 g per cu-cm, find the weight of the wire.

Answer 1

Diameter of copper wire = 6 mm, ie its radius = 3 mm

Length of cylinder = 18 cm = 180 mm
Diameter of cylinder = 49 cm = 490 mm

Number of turns of copper wire $=\frac{180}{6}=30$

length of one turn $=2\pi r=2\pi \left(\frac{490}{2}\right)=\frac{22}{7}\times 490=1540mm$

So total length of copper wire $=30\times 1540=46200mm$

Therefore volume of copper wire $=\pi r^{2}h=\pi \times (3{)}^2\times 46200=1305612m{m}^3$

Volume in $c{m}^3=1305.612c{m}^3$

Specific gravity of wire $=8.8g/c{m}^3$

So weight of wire $=1305.612\times 8.8=11489.3856=11489.38kg$