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Math Help - Maths problem

  1. #1
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    Smile 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.


    Awaiting for your help.

    Thanks a lot

    Dan
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  2. #2
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    Quote Originally Posted by DannyL View Post
    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:

    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
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