Question
A solid hemisphere of radius 6 cm is melted and recast
into small solid right circular cones each of radius 3 cm and height 8 cm. How many cones are formed?Solution
Volume of hemisphere = (2/3)πr³ = (2/3)π × 6³ = (2/3)π × 216 = 144π Volume of one cone: V = (1/3)πr²h = (1/3)π × 3² × 8 = (1/3)π × 9 × 8 = 24π Number of cones = 144π / 24π = 6.
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