Consider a circle of radius r. Answer the following questions about its plane regions.
a. (i) Define (a) a sector of a circle and (b) a segment of a circle.
b. (ii) Explain, without using any numerical calculation, why the area of a sector that subtends a central angle θ degrees at the centre must be directly proportional to θ.
c. (iii) Using your explanation in part (ii), obtain an expression for the area of such a sector in terms of r and θ. State clearly any proportionality constant you introduce.