Question

The diameter of a copper sphere is 6cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 36cm, find its radius [Take π=2.14]

Answer 1

Diameter of a copper sphere = 6 cm

So, Radius of copper sphere = 3cm

= 36π cm³

Length of wire = 36cm

Let the radius of wire be R cm

Volume of wire = πR²h

=πR²×36

But the volume of wire = volume of sphere

⇒ 36πR² = 36π

⇒ R² = 1

⇒ R = 1cm [taking positive root, because radius can’t be negative]

Hence, the radius of wire is 1cm