Question

Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic centimeter of copper weighs 8.4 g.

Answer 1

ANSWER:
Mass of copper wire = 13.2 kg = 13.2 × 1000 = 13200 g
(1 kg = 1000 g)

Volume of 8.4 g of copper wire = 1 cubic cm
∴ Volume of 13200 g (or 13.2 kg) of copper wire = $\frac{13200}{8.4}c{m}^3$
Let the length of the copper wire be l cm.
Radius of the copper wire, r = $\frac{4}{2}=2mm=0.2cm$
∴ The volume of the copper wire = $\pi r^{2}l=\frac{22}{7}\times {0.2}^{2}lc{m}^3$
⇒$\frac{22}{7}\times {0.2}^{2}lc{m}^3=\frac{13200}{8.4}$
⇒l=12500 cm
⇒l=125 m