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

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125 m

234 m

453 m

256 m

answer is A.

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Detailed Solution

It is given copper wire of weight 13.2 kg and diameter 4 mm and 1 cubic cm of copper weighs 8.4 gm.
We know that, 1 cm = 10 mm
Diameter of the wire = 4 mm
Diameter of the wire = 0.4

cm

Let

h

be the length of the wire.
Radius (r) is,

r = 0.4 2 ⇒ r = 0.2 cm

Volume of wire =

π r 2 h

⇒ V o l u m e o f w i r e = 227 × 0.2 2 × h

V o l u m e o f w i r e = 227 × 0.04 × h c m 3

Since, 1 cubic cm of copper weighs 8.4 gm.
So, Total weight =

227 × 0.04 × h × 8.4 g m

Apply the given condition.

⇒ 227 × 0.04 × h × 8.4 = 13.2 × 1000

(1kg=1000g)

⇒

h =

13.2 × 1000 × 7 22 × 0.04 × 8.4

⇒ h = 132 × 1000 × 7 × 100 × 10 10 × 22 × 4 × 84

⇒ h

=12500

cm

We know, 1m=100 cm

⇒ h

= 12500100 m

⇒ h

=125

m

Therefore, the length of the copper wire is 125

m

.
Hence option (1) is correct.

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