Question

2) 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 cones submerged.​

Answer 1

Volume of each of solid cones is 246.3 cm^3

1. The volume of the original cone is given by

V=(1/3)*(pi)*(r^2)*h   [formula for volume of a cone and diameter=16.8 then radius=8.4]

V=(1/3)*3.14*(8.4^2)*20

V=1477.805 cm^3.

2. Now let's find the volume of water displaced o overflown

Volume of Water overflown=(1/3)*V=(1/3)*1477.805      

Volume of Water overflown=492.601 cm^3.

3. From Archimedes principle volume of solid submerged completely is equal to volume of water displaced. Let's assume volume of smaller cones as V1. As there are two smaller cubes submerged

2*V1=Volume of Water overflown=492.601

V1=492.601/2

V1=246.3 cm^3.

So the volume of each of smaller cones is 246.3