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Math Help - Simpson's method

  1. #1
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    Simpson's method

    a water tower is 24m high and circular in plan. The inside radii ofthe tower at different heights are given in the follow table:

    Height(metres) 0 6 12 18 24
    Radii(metres) 10 8 7 6 6.5

    Using a stible method find the capacity of the tower in cubic metres.

    working out showing too would be greatly appreciated!
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  2. #2
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    Quote Originally Posted by jaswinder View Post
    a water tower is 24m high and circular in plan. The inside radii ofthe tower at different heights are given in the follow table:

    Height(metres) 0 6 12 18 24
    Radii(metres) 10 8 7 6 6.5

    Using a stible method find the capacity of the tower in cubic metres.

    working out showing too would be greatly appreciated!
    What do you mean by "stible" method?
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  3. #3
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    Quote Originally Posted by ticbol View Post
    What do you mean by "stible" method?
    It's a typo he meant to write: "using a suitable method".

    RonL
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  4. #4
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    Quote Originally Posted by jaswinder View Post
    a water tower is 24m high and circular in plan. The inside radii ofthe tower at different heights are given in the follow table:

    Height(metres) 0 6 12 18 24
    Radii(metres) 10 8 7 6 6.5

    Using a stible method find the capacity of the tower in cubic metres.

    working out showing too would be greatly appreciated!
    By a suitable method I will assume that Simpsons rule is required.

    V = integral pi r^2 dh, h=0..24

    Simpson's rule tells us that:

    integral f(x) dx a,b ~= h/3 [f(x0) + 4*f(x1) + 2*f(x2) + ... + 4*f(x(n-1)) +f(xn)]

    where h=(b-a)/n.

    So here we have h=6, n=4, and so:

    V ~= 2 [(pi 10^2) + 4*(pi 8^2) + 2*(pi 7^2) + 4*(pi 6^2) +(pi 6.5^2)] ~= 4022.8 cubic metres.

    RonL
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