Question
A hemisphere of radius 10 cm is melted and recast into
the shape of a cone with a base diameter of 10 cm. Find the height of the cone.Solution
Volume of the hemisphere = (2/3)πr³ Volume of the cone = (1/3)πr²h Since the volume remains constant, (2/3)π(10)³ = (1/3)π(5)²h Simplifying: (2/3)π(1000) = (1/3)π(25)h (2000) = (25)h h = 2000 / 25 = 80 cm Correct Option: b
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