The $ \frac{3}{4} $ th part of a conical vessel of internal radius $ 5 \mathrm{~cm} $ and height $ 24 \mathrm{~cm} $ is full of water. The water is emptied into a cylindrical vessel with internal radius $ 10 \mathrm{~cm} $. Find the height of water in cylindrical vessel.

Given:

The \( \frac{3}{4} \) th part of a conical vessel of internal radius \( 5 \mathrm{~cm} \) and height \( 24 \mathrm{~cm} \) is full of water. The water is emptied into a cylindrical vessel with internal radius \( 10 \mathrm{~cm} \).

To do:

We have to find the height of water in cylindrical vessel.

Solution:

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

$=\frac{1}{3}\times3.14\times 5\times5\times24$

$=628\ cm^3$

Water filled$=\frac{3}{4}\times 628=3\times 157$

$=471\ cm^3$

This volume of water is filled in the cylinder.

Volume of cylinder$=\pi r^2h$

$\Rightarrow 471=3.14\times 10\times 10\times h$

$\Rightarrow h=\frac{471}{314}$

$\Rightarrow h=1.5\ cm$

Therefore, the height of the water level in the cylindrical vessel is $1.5\ cm$.

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Updated on: 10-Oct-2022

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