Question
A cylindrical vessel of internal radius 3 cm contains
some water. When a solid metal sphere is completely immersed in it, the water level rises by 4 cm. What is the radius of the sphere? (Take π as common in both volumes; no need to evaluate numerically.)Solution
ATQ, Increase in water volume = volume of displaced water = volume of sphere. Increase in cylinder volume: V_cylinder = πR²h = π × 3² × 4 = 36π cm³. Volume of sphere = (4/3)πr³. Equate: (4/3)πr³ = 36π (4/3)r³ = 36 ⇒ r³ = 36 × 3/4 = 27 ⇒ r = 3 cm.
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