Mathematics

Problem

Consider a circle with centre

O

and radius

r

. An arc

AB

of the circle subtends a central angle of

\theta

degrees at

O

. a. (i) State the relation between the length of arc

AB

and the circumference of the circle. b. (ii) Explain why the ratio

\dfrac{\text{length of arc }AB}{\text{circumference of the circle}}

equals

\dfrac{\theta}{360^{\circ}}

. c. (iii) Using the result of part (ii), obtain an expression for the area of sector

OAB

in terms of

r

and

\theta

. Give your answer in square units.