Question
A solid hemisphere of radius 7 cm is melted and recast
into small solid spheres each of radius 3.5 cm. How many such small spheres can be made?Solution
Volume of a hemisphere = (2/3)πr³ For radius 7 cm: V_hemi = (2/3)π × 7³ = (2/3)π × 343 Volume of a sphere of radius 3.5 cm ( = 7/2): V_sphere = (4/3)π(7/2)³ = (4/3)π × 343/8 = (343/6)π Number of spheres = V_hemi / V_sphere = [(2/3)π × 343] / [(343/6)π] = (2/3) / (1/6) = (2/3) × 6 = 4 So 4 spheres.
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