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Math Help - Need help with slicing shapes in planes

  1. #1
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    Need help with slicing shapes in planes

    Since I can't draw the picture I am given, I will describe the nature of the problem to see if anyone can help me out. I am given a solid, right circular cone. The cone is sliced perpendicular to its base through its vertex and the center of its base. Then I am asked which of the answer choices best represents the plane section (The section that is cut is shaded. So the plane section is the section of the cone that hasn't been cut, I assume.) The answer is what looks like a triangle (kind of like a flattened cone, one-dimensional). Does anyone know why this is the answer? My only guess is that after the cone was cut, they "flattened the edges out" and it looked like a triangle, but I'm a bit confused.
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    MHF Contributor Siron's Avatar
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    Re: Need help with slicing shapes in planes

    Yes, I think something like that, if you slice (the way described) a cone in two pieces the plane section will look like a triangle, I think the most important thing in this case is trying to imagine it.
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    Junior Member BERMES39's Avatar
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    Re: Need help with slicing shapes in planes

    May be this will help.
    Attached Thumbnails Attached Thumbnails Need help with slicing shapes in planes-scan0004.jpg  
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    Re: Need help with slicing shapes in planes

    Why would the bottom not be rounded though?
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    Re: Need help with slicing shapes in planes

    Quote Originally Posted by benny92000 View Post
    Why would the bottom not be rounded though?
    the bottom of the vertical slice is the diameter of the cone's circular base ... it's a line segment.

    Cross-section - Geometry - Math Dictionary

    scroll down to the example
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    Re: Need help with slicing shapes in planes

    I read the link.. I understand how the "front" of the cross section would look like a triangle.. That is evident. But I don't understand what happens to the "back side of it," the 3-dimensional side, that would make the whole object a flat triangle.
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    Re: Need help with slicing shapes in planes

    Quote Originally Posted by benny92000 View Post
    I read the link.. I understand how the "front" of the cross section would look like a triangle.. That is evident. But I don't understand what happens to the "back side of it," the 3-dimensional side, that would make the whole object a flat triangle.
    there is no front and back side ... the cross-section is a plane figure (two dimensions only) , an isosceles triangle.
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    Re: Need help with slicing shapes in planes

    .
    Last edited by Whiskyfied; March 29th 2012 at 02:29 AM. Reason: thought about it
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