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Math Help - Help with ratio of volume of similar solids.

  1. #1
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    Help with ratio of volume of similar solids.

    A wooden cone is cut into 3 parts, A,B and C by 2 planes parallel to the base. The height of the 3 parts are equal.find
    i. The ratio of volume of a,b,c
    ii. The ratio of the base area of part a,b,c

    Please show the working. Really have no clue on how to do it.
    i could draw the diagram but i have no idea how to get the answs
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  2. #2
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    Re: Help with ratio of volume of similar solids.

    Am I correct in assuming that since you want the figures to be similar, you're not cutting the cone into three parts (which would give a single cone and two frustrums), you're creating three cones, correct?
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    Re: Help with ratio of volume of similar solids.

    Nope. Its like this:
    /\
    /--\
    /----\
    /____\.
    So basically 1 cone on top. 2 trapizuim of different
    Size. But the height of the a:cone b:small trapizuim
    c: big trapizuim are the same.
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    Re: Help with ratio of volume of similar solids.

    ..no given numbers
    Last edited by Aroperalta; January 27th 2013 at 05:08 AM.
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    Re: Help with ratio of volume of similar solids.

    Hi aroperalta,
    You don;t need given numbers because you are looking for relative volumes.The top cone has a v1 = 1/3pi r^2h.The next cone V2 -1/3 (2r)^2*2h. The third cone V3=1/3pi (3r)^2*3h.Differences between them defines the trapezoid like volumes.When you write the difference equations you will see that Va,Vb,Vc are related by relative volume numbers
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    Re: Help with ratio of volume of similar solids.

    Quote Originally Posted by bjhopper View Post
    Hi aroperalta,
    You don;t need given numbers because you are looking for relative volumes.The top cone has a v1 = 1/3pi r^2h.The next cone V2 -1/3 (2r)^2*2h. The third cone V3=1/3pi (3r)^2*3h.Differences between them defines the trapezoid like volumes.When you write the difference equations you will see that Va,Vb,Vc are related by relative volume numbers
    No, that is incorrect. You need to remember that when a length (such as the height) is scaled, then the volume is scaled by the CUBE of that scaling factor.

    So that means that the top cone would be \displaystyle \begin{align*} \left( \frac{1}{3} \right)^3 V \end{align*} , etc..., where V is the original volume of the cone.
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    Re: Help with ratio of volume of similar solids.

    Quote Originally Posted by Prove It View Post
    No, that is incorrect. You need to remember that when a length (such as the height) is scaled, then the volume is scaled by the CUBE of that scaling factor.

    So that means that the top cone would be \displaystyle \begin{align*} \left( \frac{1}{3} \right)^3 V \end{align*} , etc..., where V is the original volume of the cone.
    The volume of a cone = 1/3pi r^2h r^2h is a cubic measure
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