A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.6 cm. Find the length of the wire.

Question: A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.6 cm. Find the length of the wire.

Solution:
Radius of the sphere, r = 3 cm

Volume of the sphere = (4/3) × π × r³
= (4/3) × π × 27
= 36π

Radius of the wire = 0.6 ÷ 2 = 0.3 cm

Volume of the wire = πr²l
= π × (0.3)² × l
= 0.09πl

According to the condition,
0.09πl = 36π
⇒ 0.09l = 36
⇒ l = 36 ÷ 0.09
⇒ l = 400 cm
⇒ l = 4 m

∴ The length of the wire = 4 m.