The diameter of a solid sphere is 3 cm. It is melted and drawn into a wire of diameter 8 mm. The length of the wire is:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 28.125 cm.
Volume of a sphere = (4/3) × π × r³
Volume = (4/3) × π × (1.5)³ = (4/3) × π × 3.375 = 4.5π cm³
Let the length of the wire be L cm
Volume of wire (cylinder) = π × r² × L = π × (0.4)² × L = π × 0.16 × L
⇒ 4.5π = π × 0.16 × L
⇒ 4.5 = 0.16 × L
⇒ L = 4.5 / 0.16 = 28.125 cm