Question
A solid right circular cylinder of radius 5 cm and
height 20 cm is melted and recast into solid spheres of radius 2.5 cm. How many such spheres can be made?Solution
Volume of cylinder = πr²h = π × 5² × 20 = 500π cm³ Volume of one sphere (r = 2.5 = 5/2): V = (4/3)πr³ = (4/3)π × (5/2)³ = (4/3)π × 125/8 = (500/24)π = (125/6)π cm³ Number of spheres = 500π / [(125/6)π] = 500 × 6 / 125 = 24 So, 24 spheres.
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