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Find radius of bowl at certain height

  1. May 21, 2012 #1
    1. The problem statement, all variables and given/known data
    A bowl has radius of 16 cm at the top of it (the largest diameter) and diameter of 8 cm at the bottom of it (the smallest diameter). Find the diameter at position:
    a. 1/4 height
    b. 1/2 height
    c. 3/4 height


    2. Relevant equations
    not sure, maybe:
    trigonometry
    similarity


    3. The attempt at a solution
    There is no picture attached to the question so I assume that the bowl has circular side, not a straight one like plastic cup (hope I explain what I meant clear enough).

    So, how to find the radius? I think trigonometry and similarity can't be used because of the circular side...

    Thanks
     
  2. jcsd
  3. May 21, 2012 #2
    The question is a bit vague. For all I know, the bowl could be fashioned like this. Or, like this one. Assuming their upper and lower radii are equal, their radii at half their height will definitely not be the same.

    So, since you aren't given the curvature of the bowl (the side curvature) I don't think you can find out an answer. Or, you need to take it like a straight side(which I suspect is what the question is about) and use simple trigonometry and similarity to solve.
     
  4. May 21, 2012 #3

    tiny-tim

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    Science Advisor
    Homework Helper

    hi songoku! :smile:
    no, i'd go for the plastic cup (a cone) …

    there can't be a unique solution in any other case (eg a sphere)!​
     
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