Question

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

Answer 1

Since we know the weight and the volume of copper,  we can calculate its density.
\[\text{ density of copper }= \frac{\text{ weight }}{\text{ volume }} = \frac{8 . 4\text{ gram }}{1 {cm}^3} = 8 . 4\frac{\text{ gram }}{{cm}^3}\]
If the weight of copper wire is 13.2 kg and the density of copper is 8.4 g/cm³, then:
Volume = Weight / Density = 13.2 kg x 1000 gram/kg / 8.4 gram/cm³ = 1571.43 cm³
The radius of copper wire is 2 mm or 0.2 cm. So, the length of the wire can be determined in the following way:
\[L = \frac{V}{\pi r^2} = \frac{1571 . 43 m^3}{\pi \left( 0 . 2 cm \right)^2} = 125050 . 01 cm = 125 m\]
Thus, the length of 13.2 kg of copper is 125 m.