Maths problem

Quote:

Originally Posted by DannyL

I need help for this problem:

A solid pyramid of height 40cm and with a square base of side 30cm is put into a cubical tank of side 40cm. The tank is then filled with water. If the pyramid is removed, find the depth of water in the tank.
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If the cubic tank is filled with water it contains:

$V_{tank} = 40^3\ cm^3 = 64,000\ cm^3$

The pyramid displaces as much water as it could contain:

$V_{pyramid} = \frac13 \cdot a_{base} \cdot height$ . With your problem the volume of the pyramid is:

$V_{pyramid} = \frac13 \cdot 30^2 \cdot 40\ cm^3 = 12,000 \ cm^3$

That means there are only $64,000 - 12,000 = 52,000\ cm^3$ water in the tank.

The base area of this water is $40^2 \ cm^2$ the volume of this water is:

$V_{water} = a_{base} \cdot h_{water}$

$52,000 = 1600 \cdot h~\implies~h=32.5 \ cm$