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Math Help - Design of ice cream container

  1. #1
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    Design of ice cream container

    Hi everyone,

    I have this assignment for school where I have to develop a new package design for an existing ice cream brand. I have to actually print and mount the design on an existing Ice Cream 16oz Pint. What I can't seem to find is a way to calculate and template the outside surface of the pint. I don't even know how to call that cut cone, is there a name for that shape?

    So basically I know the diameter and radius of both the top and bottom base/circle and the height of the pint. What I need now is to calculate and create the template where I will insert my design into to print and mount.

    The final result should look like this: (the left part)
    http://fc30.deviantart.com/fs29/i/20...by_tori927.jpg

    And the shape as you might have already realized is something like this: (but upside down)
    http://www.ficharionline.com/imagens.../img5879n3.jpg

    How do I calculate/create this? Having the height of the cup/pint and the diameters of the circles. What is the height/angel of both the top and bottom arches? Is there a software that designs this for me by inputting the measurements?
    Can anyone help me with this?
    It's pretty urgent, the deadline is almost here, I'm done with the design just need to template it, print it and mount it.

    Height: 3.622 in
    Top Diameter: 3.62 in
    Bottom Diameter: 2.93 in

    Thanks in advance,
    T
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  2. #2
    Member arpitagarwal82's Avatar
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    Your cup will cut out from a cone.
    Fig 1 is cone out of which your cup will be cut

    Fig 2 is sector of circle when cone is opened into a plane paper ( along its latent height You need is yellow portion of this sctor

    we have r, R and h

    you can calculate l and l_2

    I would like someone else to verify this.
    Attached Thumbnails Attached Thumbnails Design of ice cream container-01.jpg  
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  3. #3
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    It DOES look really understandable and well done, but I'm not really good with math.. I do get where you're going and what you're doing, I get the concept but I just don't know how to create it with my measurements..

    Can you tell me the exact area of the yellow area and height/angle of the arch with the measurements I gave you? Is it possible?

    Thank you SO much for your time and help!
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  4. #4
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    I would think (and would like someone to verify) that to get the area of that arc, you would do something like:

    (area of the larger circle - area of the smaller circle) * (angle from center of circle to left and to right / 360 )

    For example if the outer circle is diameter 5" and inner is diameter 3" and the angle is 45 degrees, the area (I believe) would be calculated like this:

    (5*pi - 3*pi) * (45/360) = 0.7853 sq. in

    I MAY BE WRONG... but it makes sense in my tiny brain.
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  5. #5
    Member arpitagarwal82's Avatar
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    Radius of outer circle is l
    radius of inner circle is l - l_2

    angle of sector is (R * 360)/l degree

    The image above contains all the equations to calculate l, l_2
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