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Volume of Hollow Cylinder

A vessel in t...

Question

A vessel in the form of an inverted cone is filled with water to the brim. It's height is 20 cm 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. What is the volume of each of the solid cone submerged?

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Solution

We have, Height of the cone = 20 cm, diameter = 16.8 cm, radius = 16.8/2 = 8.4 cm.
Volume of water in bigger cone = 1/3 π r2 h = (1/3)(22/7)(8.4)(8.4)(20)
= 1478.4 cm3.
Volume of water overflowed = (1/3)(1478.4) = 492.8 cm3
Volume of each solid cone = (1/2)(492.8) = 246.4 cm3.

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