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Math Help - Frustum of cone question and enlargement of triangle length. pic included - gcse math

  1. #1
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    Frustum of cone question and enlargement of triangle length. pic included - gcse math

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting - frustum of cone

    Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting - triangle question

    At a complete loss. Please do not simply tell me the answer, but give me a step-by-step process of how you got to that answer.
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  2. #2
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    That "triangle" is NOT a triangle!
    Agree with y = 2.5; that leaves a triangle dimensions 3.5-7-11 which is impossible...OK?
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  3. #3
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    On the cone problem.
    I assume you know the volume of a cone = pi r^2 h / 3

    volume larger cone = pi r^2 2h / 3 = 360 ; simplify to get: p1 r^2 = 540 [1]

    volume smaller cone = pi (r/2)^2 h ; simplify, substitute [1] to get volume = 45

    cup volume is difference...OK?
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  4. #4
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    Hello, lFrenzied!

    Frustum of cone

    The a diagram shows a paper cup of height h.
    It is part of a cone of height 2h and volume 360\text{ cm}^2.

    Find the volume of the cup.

    Code:
          :       :  2r   :
          *-------+-------* -
           *      :      *  :
            *    h:     *   :
             *    : r  *    :
              *---+---*    2h
               *  :  *      :
                *h: *       :
                 *:*        :
                  *         -

    \text{The volume of the entire cone is: }\:V_1 \:=\:\tfrac{\pi}{3}(2r)^2(2h) \:=\:\tfrac{8\pi}{3}r^2h\text{ cm}^3

    \text{The volume of the small cone is: }\:V_2 \:=\:\tfrac{\pi}{3}(r^2)(h) \:=\:\tfrac{\pi}{3}r^2h\text{ cm}^3

    \text{The volume of the cup is: }\:V \:=\:V_1 - V_2 \:=\:\tfrac{8\pi}{3}r^2h - \tfrac{\pi}{3}r^2h \:=\:\tfrac{7\pi}{3}r^2h\text{ cm}^3


    \text{We see that the cup has }\tfrac{7}{8}\text{ the volume of the entire cone.}


    \text{Therefore: }\;V \;=\;\tfrac{7}{8}(360) \:=\:315\text{ cm}^3.

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  5. #5
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    Another way
    V of smaller cone / V of larger cone= (1/2 r )^2*h / r^2*2h = 1/8 Cup = 7/8 of 360
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