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Math Help - Need help with analytical method

  1. #1
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    Need help with analytical method

    Hi,
    In the attachment I have arrived at the correct answer but my tutor tells me there are mistakes in the last part of my analytical method as shown in the box.
    Can someone have a look and tell me whats wrong with it.
    Attached Thumbnails Attached Thumbnails Need help with analytical method-26-01-2010-09-44-03_0043.jpg  
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  2. #2
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    Dear manich44,

    The correct answer is h=3.14m. But I do not quite understand the analatical method that you have used. Of course,

    3.14^3\neq{30.98+274.8-305.73}

    If you could please explain the analytical method that you had used to get the answer maybe I will be able to help you further.
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  3. #3
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    Re Analytical method

    Hi,


    Thanks for the reply.

    Task was to find the height of a dome if the Radius was was 5.4m and volume of air space underneath = V is 160mcub

    Based on the previous task...sphere cap radius = 4.6m and sphere cap height = 2.8m,the volume of air space under the dome was 104.5605811mcubed

    so back to the box section of the attachment,if vol is now 160mcub then h has to be more than 2.8m,so I took initial guess at 2.9 and then trial and error and eventually got to 3.141cub= 30.98
    Must be an easier way...
    Mark..
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  4. #4
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    Then your tutor is probably suggesting that you should explain, in your working, exactly what kind of trial and error you used.
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  5. #5
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    Quote Originally Posted by manich44 View Post
    Hi,


    Thanks for the reply.

    Task was to find the height of a dome if the Radius was was 5.4m and volume of air space underneath = V is 160mcub

    Based on the previous task...sphere cap radius = 4.6m and sphere cap height = 2.8m,the volume of air space under the dome was 104.5605811mcubed

    so back to the box section of the attachment,if vol is now 160mcub then h has to be more than 2.8m,so I took initial guess at 2.9 and then trial and error and eventually got to 3.141cub= 30.98
    Must be an easier way...
    Mark..
    Dear manich44,

    Of course your trial and error method is incorrect. You have got a depressed cubic equation ( h^3+87.48h-305.73=0). To know how to solve it please refer The "Cubic Formula" There you would find all the necessary details about how to solve cubic equations.

    Hope this helps.
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