Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.
Given data is as follows:
Weight of copper wire = 13.2 kg
Diameter = 4 mm
Density = 8.4 gm/cm3
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/cm3. 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/cm3 . Therefore, we have,
Weight of copper wire = 13.2 × 1000 gm
= 13200 gm
We know that,
Volume × Density = Weight
`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.
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