Find the length of 13.2 kg of copper wire of diameter 4 mm,
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.

Solution:

Given data is as follows:

Weight of copper wire = 13.2 kg

Diameter = 4 mm

Density $=8.4 \mathrm{gm} / \mathrm{cm}^{3}$

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 $\mathrm{r}$ from millimeter to centimeter, since density is in terms of $\mathrm{gm} / \mathrm{cm}^{3}$. Therefore,

r = 210 cm

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

Weight of copper wire = 13.2 × 1000 gm

= 13200 gm

We know that

Volume × Density = Weight

Therefore, $\pi r^{2} h \times 8.4=13.2$

22/7 × 2/10 × 2/10 × h × 8 .4

h = 12500 cm

h = 125 m

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

 

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