A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm. What is the inner…

Question

A hollow metallic sphere has outer radius 10 cm and is melted to make 50 smaller solid spheres of radius 2 cm. What is the inner radius of the original sphere?

1. A. 8.43 cm (Correct answer)
2. B. 7.48 cm
3. C. 5.46 cm
4. D. 6.44 cm

Correct Answer

Option A — 8.43 cm

Detailed Solution & Explanation

The correct answer is 8.43 cm.

Key Points

• Melting conserves volume: (hollow shell) = 50 × (small solid sphere).
• With outer radius 10 and small radius 2:
• (4/3)π(10³ − r³) = 50·(4/3)π·2³ → 1000 − r³ = 50·8 = 400 → r³ = 600 → r = ∛600 ≈ 8.43 cm.
• The 4/3·π cancels on both sides, so 'melting and recasting' problems reduce to equating the plain radius-cubed terms.