Question

A rectangular vessel of dimensions $20cm\times 26cm\times 11cm$ is full of water. This water is poured into a conical vessel. The top of the conical vessel has its radius $10cm$. If the conical vessel is filled completely, determine its height (Use $\pi =22/7$)

Answer 1

Given,

Dimensions of the cuboid vessel $l\times b\times h=20cm\times 26cm\times 11cm$

The radius of the top of the conical vessel $r=10cm$

Volume of cuboid vessel $V=20\times 26\times 11c{m}^3$

$V=5720c{m}^3$

Given, if the conical vessel is filled completely.

Volume of conical vessel = Volume of cuboid vessel

$\Rightarrow \frac{1}{3}\pi r^{2}h=5720$

$\Rightarrow h=\frac{3\times 5720}{\pi r^2}$

$\Rightarrow h=\frac{17160}{\frac{22}{7}\times {10}^2}$

$\Rightarrow h=\frac{17160\times 7}{22\times 100}$

$\Rightarrow h=\frac{120120}{2200}$

$\Rightarrow h=54.6$

Hence, the height of the conical vessel is $54.6cm$