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A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water upto $1\ cm$ from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
Given:
A rectangular container, whose base is a square of side $5\ cm$, stands on a horizontal table, and holds water upto $1\ cm$ from the top.
When a cube is placed in the water it is completely submerged, the water rises to the top and $2$ cubic cm of water overflows.
To do:
We have to find the volume of the cube and also the length of its edge.
Solution:
Base of the container $= 5\ cm \times 5\ cm$
Volume of the water raised and overflowed $= 5 \times 5 \times 1 + 2$
$= 25 + 2$
$= 27\ cm^3$
This implies,
Volume of the cube $= 27\ cm^3$
Therefore,
The edge of the cube $=\sqrt[3]{27}$
$=\sqrt[3]{3^{3}}$
$=3 \mathrm{~cm}$
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