A solid metal cone of height 30 cm and radius of base 10 cm is melted in to the form of a solid sphere. Find the radius of the sphere (in cm).
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Correct answer: D
Explanation
The correct answer is option 4 i.e 5∛6.
Volume = (1/3) × π × r² × h
Volume of the cone = (1/3) × π × (10)² × 30 = (1/3) × π × 100 × 30 = 1000π cm³
The volume of the sphere = (4/3) × π × r³
The volume of the cone is equal to the volume of the sphere, so:
⇒ 1000π = (4/3) × π × R³
⇒ 1000 = (4/3) × R³
⇒ 3000 = 4 × R³
⇒ R³ = 3000 / 4 = 750
R = ∛750 = 5∛6 cm