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  • Perplex
    IB Math AIHL
    /
    Differentiation
    /

    Problem Bank

    [Maximum mark: 9]

    A farmer has ​16​ meters of fencing, and wants to use it to create an enclosure for his sheep to graze in. He wants the enclosure to have a rectangular section and a semi-circular section with radius ​r, as illustrated in the diagram below.


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    1. Give an expression for the area of the enclosure in terms of ​r.

      [4]
    2. Find the maximum possible area of the enclosure.

      [5]

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