NumericalHard4 marks
A solid is in the shape of a hemisphere of radius 7 cm, surmounted by a cone of height 4 cm. The solid is immersed completely in a cylindrical container filled with water to a certain height so that the solid is completely submerged in water. If the radius of the cylinder is 14 cm, find the rise in the water level.
Topic: Mensuration of solids
Previous-year question practice database
Answer
Exam answer
Rise in water level = 1.5 cm.
Explanation
Volume displaced = volume of hemisphere + cone = (2/3)π7³ + (1/3)π7²·4 = 294π cm³. Rise h = 294π/(π14²)=1.5 cm.
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