# Maths problem

• Mar 4th 2008, 07:48 AM
DannyL
Maths problem
Hello to all of you,

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.

Thanks a lot

Dan
• Mar 4th 2008, 08:13 AM
earboth
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.
...

If the cubic tank is filled with water it contains:

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

The pyramid displaces as much water as it could contain:

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

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

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

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

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

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