An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.

Here is a vessel in the form of an inverted cone is filled with water to the brim. Its height and diameter is given. Two equal solid cones are dropped in it so that they are fully submerged.

What is the volume of each of the solid cone submerged?

This is the Question Number 17, Exercise 17.5 of M.L Aggarwal.

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# A vessel in the form of an inverted cone is filled with water to the brim. Its 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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Given height of the cone, h = 20 cmDiameter of the cone = 16.8 cmRadius of the cone, r = 16.8/2 = 8.4 cmVolume of water in the vessel = (1/3)r^{2}h= (1/3)×8.4^{2}×20= (1/3)×(22/7)×8.4 ×8.4 ×20= 1478.4 cm^{3}One third of volume of water in the vessel = (1/3)× 1478.4= 492.8 cm^{3}One third of volume of water in the vessel = Volume of water over flownVolume of water over flown = volume of two equal solid cones dropped into the vessel.volume of two equal solid cones dropped into the vessel = 492.8 cm^{3}Volume of one solid cone dropped into the vessel = 492.8/2 = 246.4 cm^{3}Hence the volume of each of the solid cone submerged is 246.4 cm^{3}.