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Math Help - Maximum aea of rectangular field surmounted by two semicircular fields.

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    Maximum aea of rectangular field surmounted by two semicircular fields.

    A rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 200 meters. Answer the following:
    a) Express the area of the rectangular field (shaded green) in terms of r
    Area =

    b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
    Maximum area = (square meters)


    I do not know where to even begin on this problem if anyone could help me. Any explanation as to what strategy i should use would be awesome.
    Last edited by mr fantastic; June 26th 2011 at 09:18 PM. Reason: Re-titled.
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  2. #2
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    Re: Can anyone help me with this problem?

    First step is to draw a picture of the shapes decribed.

    Then label the picture with the information for x and 2r.

    Then make an expression for the perimeter with this information.

    I.e. x+x+.... = 200.
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  3. #3
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    Re: Maximum aea of rectangular field surmounted by two semicircular fields.

    Quote Originally Posted by willjones2010 View Post
    A rectangular field with base x and height 2r is surmounted by two semicircular fields, as shown in the diagram below. The external perimeter of the fields (solid blue track) is 200 meters. Answer the following:
    a) Express the area of the rectangular field (shaded green) in terms of r
    Area =

    b) Determine the maximum area enclosed by the rectangular field. (Type "pi" if you need it, or look in the MathPad Greek list. Decimal approximations are marked incorrect.)
    Maximum area = (square meters)


    I do not know where to even begin on this problem if anyone could help me. Any explanation as to what strategy i should use would be awesome.
    Are you expected to use calculus?
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