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Question
A vessel in the form of an inverted cone is filled with water to the brim: Its height is 20 cm and the 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. What is the volume of each of the solid cones submerged?
Solution
Height = 20 cm, diameter = 16.8 cm or radius = `16.8/2` = 8.4 cm.
Volume of water in bigger cone = `1/3`πr2h
= `1/3 xx 22/7` x 8.4 x 8.4 x 20
= 1478.4 cm3
Volume of water overflows when two equal cone is submerged = `1/3` x 1478.4
= 492.8 cm3
∴ Volume of two equal cones = 492.8
So volume of each cone = `1/2` x 492.8 = 246.4 cm3.
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