A vessel in the form of a 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?

The correct answer is: 246.4 cm³

We have given the dimensions of a inverted cone filled with water

Height, h = 20 cm

Diameter, d = 16.8 cm

Radius, r = 16.8 / 2 = 8.4
We have to find the volume of the given cone
We know that
Volume of a cone = (1/3)πR²H

= (1/3)(3.14)(8.4 x 8.4)(20)

= (1/3)(3.14) (70.56 x 20)

= (1/3)(3.14)(1411.2)

= 3.14 x 470.4

= 1478 cm³
When the two equal solid cones are dropped in the cone one third of water in original cone overflows
Therefore, Volume of both cones dropped = (1/3) Volume of original cone

= (1/3) 1478

= 492.8
As the both cones are equal , their volume is equal . Let V be the volume of one cone

2V = 492.8

V = 246.4
Therefore the volume of one dropped cone is 246.4 cm³.
Therefore, the correct option is b)246.4 cm³ .