A sector of a circle, center O and radius 4.5m, is shown in the following diagram. Diagram not to scale. (a) Find the angle AOB. Find the area of the shaded segment. [8] A square field with side 8m has a goat tied to a post in the center by a rope such that the goat can reach all parts of the field up to 4.5m from the post. Diagram not to scale. (i) Find the area of a circle with radius 4.5m. (ii) Find the area of the field that can be reached by the goat. [5] Let V be the volume of grass eaten by the goat, in cubic meters, and r be the length of time in hours that the goat has been in the field. Find the value of r at which the goat is eating grass at the greatest rate. [2]
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