Question

A vessel in the form of an inverted cone is filled with water to the brim. Its height is $32cm$ and diameter is $25.2cm.$ 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?

Answer 1

Let the volume of each cone be $V.$

Given:-

Height of the vessel, $h=20cm$

Radius of the vessel, $r=\frac{16.8}{2}cm$

$=8.4cm$

Volume of the vessel $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\times \frac{22}{7}\times 8.4\times 8.4\times 20$

$=3.36\times 440$

$=1478.4c{m}^3$

According to question,

$2\times V=\frac{1}{3}\times 1478.4c{m}^3$

$2V=492.8c{m}^3$

$V=246.4c{m}^3$