Question
A sphere is melted and recast into 8 smaller spheres of
equal size. If the radius of the original sphere is 12 cm, find the radius of each smaller sphere.Solution
Volume of the original sphere = (4/3)πR³ = (4/3)π(12³) = (4/3)π(1728) = 2304π. Volume of each smaller sphere = 2304π / 8 = 288π. Let the radius of each smaller sphere be r. Volume = (4/3)πr³. (4/3)πr³ = 288π. r³ = 288 × (3/4) = 216. r = ³√216 = 6 cm. Correct option: a
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