The $\frac{3}{4}$th part of a conical vessel of internal radius $5\ cm$ and height $24\ cm$ is full of water. The water is emptied into a cylindrical vessel with internal radius $10\ cm$. Find the height of water in cylindrical vessel.
Given: The $\frac{3}{4}$th part of a conical vessel of internal radius $5\ cm$ and height $24\ cm$ is full of water. The water is emptied into a cylindrical vessel with internal radius $10\ cm$.
To do: 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 fills the cylinder
Volume of cylinder$=\pi r^2h$
$\Rightarrow 471=3.14\times 10\times 10\times h$
$\Rightarrow h=\frac{471}{314}$
$\Rightarrow h=1.5\ cm$
$\therefore$ Height of water level in cylindrical vessel $=1.5\ cm$.
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