A shape consists of a rectangular base with a semicircular top, as shown. a. Given that the

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A shape consists of a rectangular base with a semicircular top, as shown.


a. Given that the perimeter of the shape is 40 cm, show that its area, A cm2, is given by the formula


image


where r cm is the radius of the semicircle.


b. Hence find the maximum value for the area of the shape.


image

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