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Question

The diameter of metallic sphere is 6cm. The sphere is melted and drawn into a wire of uniform cross-section. If the lengths of the wire is 36m, find its radius.

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Solution

We have
Diameter of the sphere =6cm

Radius of the sphere=62=3cm

Volume of the sphere =43×π×33cm3=36πcm3[V=43π33]

Let the radius of the cross-section of wire be r cm

It is given that the length of the cylindrical shaped wire is 36m

Volume of the wire =(πr2×3600)cm3[V=πr2h]

since metallic sphere is converted into cylindrical shaped wire. Therefore,
Volume of the wire = Volume of the sphere

r2=36π3600π=1100r=110cm=1mm

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