Question
A solid metal sphere of radius 6 cm is melted and recast into solid hemispheres of radius 3
cm. How many such hemispheres are formed?
Solution
Volume of sphere: V_sphere = (4/3)πR³ = (4/3)π × 6³ = (4/3)π × 216 = 288π Volume of one hemisphere (radius 3 cm): V_hemi = (2/3)πr³ = (2/3)π × 3³ = (2/3)π × 27 = 18π Number of hemispheres = 288π / 18π = 16.
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