Question
A solid right circular cone of radius 8 cm and height 4
cm is melted and recast into a solid sphere. What is the radius of the sphere (in cm)?Solution
ATQ, Volume of cone = (1/3)πr²h = (1/3)π × 8² × 4 = (1/3)π × 64 × 4 = (256/3)π. Volume of sphere = (4/3)πR³. Equate: (4/3)πR³ = (256/3)π ⇒ 4R³ = 256 ⇒ R³ = 64 ⇒ R = 4 cm.
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