The radius of a solid sphere of a metal is 3 cm. How long wire of diameter 4 mm can be drawn from it?

The core idea is conservation of volume. The metal in the sphere is simply re-shaped into a cylinder (the wire), so the volume stays the same.

Volume of sphere = (4/3)πr³ = (4/3)π(3)³ = 36π cm³.

The wire has diameter 4 mm, so radius = 0.2 cm and cross-section = π(0.2)² = 0.04π cm².

Length = volume / cross-section = 36π / 0.04π = 900 cm = 9.0 m. So option B is correct.

• A (8.8 m), C (9.6 m), D (9.1 m): None of these comes out of the exact calculation. They are the results of a wrong radius, a unit slip, or rounding π too early and carrying the error through.

This is a mensuration-with-units question that appears in UPPSC and other state PCS papers. The same volume-conservation logic is used for melting, recasting and drawing wires, so it is worth practising in a few variations.

Trap: Using the 4 mm diameter directly as the radius, or mixing mm with cm, which changes the answer by a factor of 4 or 100.