Question

Find the area of a sector with a central angle of and a radius of 18.8 m

Answer 1

For a sector of theta radians in a circle of radius r, the area A is:
A = r^2 theta / 2.

When theta = 2pi / 15 and r = 18.8m:
A = 18.8^2 * pi / 15
= 74.0 m^2 to 3 sig. fig.

There are 2pi radians in one revolution.
Thus, from the area pi r^2 of the circle, the area of a sector subtending theta at the centre is:
(theta / 2pi)(pi r^2)
= r^2 theta / 2.