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

#### Solution

Given data is as follows:

Weight of copper wire = 13.2 kg

Diameter = 4 mm

Density = 8.4 gm/cm^{3}

We have to find the length of the copper wire.

Given is the diameter of the wire which is 4 mm. Therefore,

r = 2 mm

Let us convert r from millimeter to centimeter, since density is in terms of gm/cm^{3}. Therefore,

r = `2/10` cm

Also, weight of the copper wire is given in kilograms. Let us convert into grams since density is in terms of gm/cm^{3 }. Therefore, we have,

Weight of copper wire = 13.2 × 1000 gm

= 13200 gm

We know that,

Volume × Density = Weight

Therefore,

`pir^2h xx 8.4 = 13.2`

`22/7 xx 2/10 xx 2/10 xx h xx 8.4 = 13200`

h = 12500 cm

h = 125m

Hence, the length of the copper wire is 125 meters.