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?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8.43 cm.
Volume of material = (4/3)π(R3 – r3) = 50 × (4/3) × π × (23)
⇒ R3 – r3 = 50 × 8 = 400
⇒ 103 – r3 = 400
⇒ 1000 – r3 = 400
⇒ r3 = 600
⇒ r = ∛600 ≈ 8.43 cm