Question

A vessel in the form of an inverted cone is filled with water to the brim. Its height is $20cm$ 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.

Answer 1

Volume of inverted cone $=\frac{1}{3}\pi r^{2}h$

$=\frac{1}{3}\pi ({\frac{16.8}{2})}^2\times 20$

$V=\frac{1}{3}\pi {\left(8.4\right)}^2\times 20$

when 2 similar cones are dropped one third of $V$ is displaced

Volume of $2$ cones $=\frac{1}{3}\times$ volume of inverted cone

$\frac{V}{3}=2\times$ (volume of immersed cone)

$\therefore$ volume of each immersed cone $=\frac{1}{3}\times \frac{1}{3}\pi {\left(8.4\right)}^2\times 20$

$=246.4{cm}^3$

Volume of each immersed cone is $246.4{cm}^3$