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Math Help - Cone

  1. #1
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    Cone

    How high should you fill a cone with height 10 cm if you are to fill half of it?
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  2. #2
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    Hello reiward
    Quote Originally Posted by reiward View Post
    How high should you fill a cone with height 10 cm if you are to fill half of it?
    This is equivalent to saying:
    Two cones have the same shape (i.e. the same angle at the vertex), and one has twice the volume of the other. The larger cone has height 10 cm. What is the height of the smaller?
    Well, if two similar solids have corresponding lengths in the ratio a: b, then their surface areas are in the ratio a^2:b^2 and their volumes are in the ratio a^3:b^3. So here, if we suppose the height of the smaller cone is h cm, then the ratio of the heights is h:10; and we know that the ratio of their volumes is 1:2. So:
    h^3:10^3 = 1:2

    \Rightarrow \frac{h^3}{1000} = \frac{1}{2}

    \Rightarrow h = \sqrt[3]{500}
    =7.94 cm (to 2 d.p.)
    Grandad
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