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2.2 cubic $dm$ of brass is to be drawn into cylindrical wire $0.25 cm$ in diameter. Find the length of the wire.

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343 m

546 m

448 m

753 m

answer is C.

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Detailed Solution

It is given a brass of 2.2 cubic dm is drawn into a cylindrical wire of diameter 0.25 cm.
Let

h

be the length of the wire.
Since, Radius =

D i a m e t e r 2

So, Radius (r) is

r = 0.25 2 ⇒ r = 0.125 cm

Since, the wire is drawn from the brass, so their volumes will be equal.
Volume of wire = Volume of brass

2.2

d m 3

= 2.2 × 10 × 10 × 10 cm 3

{1 dm = 10

cm

}

2.2

d m 3

=2200

c m 3

Since, volume of wire =

π r 2 h

So,

h = V o l u m e o f w i r e π r 2

⇒ h = 2200 227 × 0.125 2

⇒ h = 2200 × 7 22 × 0.125 × 0.125

⇒ h = 2200 × 7 × 1000 × 1000 22 × 125 × 125

⇒ h

= 44800

cm
We know that,1 m =100

cm

⇒ 44800 c m = 44800100 m

⇒ 44800 c m

= 448

m

Therefore, the length of the wire is 448

m

.
Hence option (3) is correct.

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