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Math Help - Bisection method problem #2(check answer)

  1. #1
    Member javax's Avatar
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    Bisection method problem #2(check answer)

    Hello everybody. I'm getting headache of not getting the right result.

    A trough of length L has a cross section in the shape of a semicircle with radius r. When filled with water to within a distance h of the top, the volume V of water is V = L[0.5\pi r^2-r^2\arcsin{(h/r)}-h(r^2-h^2)^{1/2}]

    Suppose L=10 ft, r=1 ft, and V=12.4 ft^3. Find the depth of water in the trough to within 0.01 ft.
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    Now I'm supposed to find h from this equation

    10[0.5\pi-\arcsin h - h(1-h^2)^{1/2}]=12.4

    and my solution is approx. 0.16(and I know it's right for the above equation) while the answer in book is 'the depth of water is 0.838 ft.'
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  2. #2
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    Your answer is correct and easily verifiable.
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  3. #3
    Member javax's Avatar
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    hihihi...long time since I posted this problem. I solved it after I reviewed the figure again and I got 10 out of 10 in num analysis . Good to know there are people like you who answer these unanswered threads!
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