Question
A sphere is melted and recast into 64 smaller spheres of
equal size. If the radius of the original sphere is 16 cm, find the radius of each smaller sphere.Solution
Volume of the original sphere = (4/3)πR³, where R = 16 cm. Volume of each smaller sphere = (4/3)πr³, where r is the radius of the smaller sphere. Since the original sphere is recast into 64 smaller spheres: (4/3)π(16³) = 64 × (4/3)πr³. Cancel (4/3)π on both sides: 16³ = 64 × r³. Simplify: r³ = 16³/64 = 16²/4 = 64. r = 4 cm. Correct answer: b. 4 cm
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