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Question

A vessel in the form of an inverted cone is filled with water to the brim. Its height is 20cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows.

Solution
Verified by Toppr

Volume of inverted cone =13πr2h
=13π(16.82)2×20
V=13π(8.4)2×20
when 2 similar cones are dropped one third of V is displaced
Volume of 2 cones =13× volume of inverted cone
V3=2× (volume of immersed cone)
volume of each immersed cone =13×13π(8.4)2×20
=246.4cm3
Volume of each immersed cone is 246.4cm3

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