Question

The diameter of a sphere is 6cm. It is melted and drawn into a wire of diameter 2mm. Find the length of the wire.

Answer 1

It is given that

Diameter of the sphere = 6cm

Radius of the sphere = 6/2 = 3cm

Diameter of the wire = 2mm = 0.2 cm

Radius of the wire = 2/2 = 1mm = 0.1 cm

Consider h cm as the required length

So we get

πr²h = 4/3 πR³

By substituting the values

(22/7) × 0.1² × h = 4/3 × (22/7) × 3³

On further calculation

h = (4/3 × (22/7) × 27)/ ((22/7) × 0.1²)

So we get

h = 36/0.01 = 3600cm = 36m

Therefore, the length of the wire is 36m.