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When a cube is completely submerged in a cylindrical jar of radius 3.5 cm containing water to a height of 8 cm,
the water level rises by 4mm. Calculate the length of one side of the cube correct to 4 significant figure
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The volume of the cube is equal to the difference of the occupied volumes in the cylinder after and before submerging.
This difference of volumes is = = 15.393791 cm^3.
In the formula, the value 0.4 represents the water level rise expressed in centimeters.
So, if the length of the cube' side is "a", then you have this equation to find "a"
a^3 = 15.393791,
which gives the solution a = = 2.4876 cm.
We only need to check that the diagonal of the cube's face is less than the cylinder's diameter.
The diagonal is = 3.5180 cm, which is less than the diameter of 2*3.5 = 7 cm.
ANSWER. The side of the cube is 2.4876 cm.
Solved.
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The basic idea of the solution is that the volume of the submerged body is the difference of occupied volumes.
This fact is known from the Archimedes era.
About Archimedes, read from these Internet sources
https://en.wikipedia.org/wiki/Archimedes
http://archimedespalimpsest.org/about/history/archimedes.php
http://www.ancientgreece.com/s/People/Archimedes/
It is really interesting reading (!)
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If you want to see many other similar and different solved problems, look into the lesson
- Water level rise in a tank after submerging bodies
in this site to make your horizon wider.
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