Question
A solid metal sphere of radius 6 cm is melted and recast
into smaller solid spheres each of radius 3 cm. How many such smaller spheres can be made?Solution
Volume of original sphere: V = (4/3)πR³ = (4/3)π × 6³ = (4/3)π × 216 = 288π Volume of one small sphere (r = 3 cm): v = (4/3)πr³ = (4/3)π × 3³ = (4/3)π × 27 = 36π Number of small spheres = 288π / 36π = 8 Answer: 8 spheres.
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