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Math Help - help me with the similarity and congruence

  1. #1
    Member helloying's Avatar
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    help me with the similarity and congruence

    A cup is in the form of an inverted square pyramid. When the depth of the water is 10cm, the volume of the water is 187.5cm³. When
    327cm³ of water is pored into the the cup, water level rises to 14cm.Find the increase in area of the water surface in the cup.Ans is 18cm²
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by helloying View Post
    A cup is in the form of an inverted square pyramid. When the depth of the water is 10cm, the volume of the water is 187.5cm³. When
    327cm³ of water is pored into the the cup, water level rises to 14cm.Find the increase in area of the water surface in the cup.Ans is 18cm²
    V = \frac{1}{3}L^2h
    where L is the length of a side of the base and h is the height. So from the first pieces of information you can find L.

    Now you add some volume. You know that the result is still going to be a square pyramid, so
    V + \Delta V = \frac{1}{3}L'^2 h
    where h'= 14~cm. You can find the new L'. Thus
    \Delta A = L'^2 - L^2

    -Dan
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