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?

Answer 1

Height = 20 cm

diameter = 16.8 cm

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 cones are 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.