Q. 55.0( 3 Votes )

# A metallic sphere of radius 15 cm is melted and a wire of diameter 1 cm is drawn from it. Find the length of the wire.

Answer :

Given.

Cylindrical wire of diameter 1 cm

Metallic spherical of radius 15 cm

Formula used/Theory.

Volume of cylinder = πr^{2}h

Volume of sphere = πr^{3}

Let the length of wire be x

Volume of cylinder = πr^{2}h

= π × ( cm) ^{2} × x

= π cm^{2}

Volume of sphere = πr^{3}

= π (15 cm) ^{3}

= 4500π cm^{3}

**Note we will not put value of π as it will be divided in next step

As we melt the metallic sphere in cylindrical wire the volume of both will be equal

∴ equating both we will get the length of wire

Volume of wire = Volume of metallic sphere

π cm^{2} = 4500π cm^{3}

x = 4500 × 4

x = 18000 cm = 180 m

∴ length of wire is 180 m

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