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Math Help - volume AND ration - similar shapes

  1. #1
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    volume AND ration - similar shapes

    Hi,
    I was stuck on a question and was wondering if anyone could help me.

    A cone is split into two pieces of equal volume. Show that the large cone is about 26% taller than the small cone
    Hint: begin by finding the volume scale factor for the two cones

    Thanks
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: volume AND ration - similar shapes

    Remember that the volume of a cone is equal to 1/3 base area times height. If the height of the taller cone is a factor x times larger than the smaller cone, then the radius of the base of the larger cone is that same factor x times larger as well, because the two cones are similar. This means the area of the base of the larger cone is x^2 times larger than the area of the base of the smaller cone - do you see whythat is? Consequently the volume of the larger cone is a factor x^3 times bigger than the volume of the smaller cone. From this - can you determine what the value of x must be be for the larger cone to be twice the volume of the smaller cone?
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  3. #3
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    Re: volume AND ration - similar shapes

    thks..i need to understand it more i think...
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