Mathematics

Problem

A circle of radius

r

is divided into

m

equal parts by radii, each subtending an angle

\theta

at the centre. (a) Express

\theta

in terms of

m

. (b) Using the fact that the area of the whole circle is

\pi r^2

, derive a general formula for the area of one such sector. (c) Hence find the exact area of a sector whose central angle is

120^\circ

in a circle of radius

6\,\text{cm}