Sectors of Circles

Three formulas that can help you find a sector of a circle are:
s=rθ where s is the arc length and θ is the central angle but s and r have to have the same units.

K=½ r²θ where k is the area of a sector and r is the radius.

K=½ rs

Ex. 1. A sector of a circle has radius 6cm and central angle .5 radians. Find its arc length and area.

Say what’s given and what you need to find.

R=6cm
θ=.5
s=?
k=?

The formula s=rθ is used first to find s which is the arc length.
S=6/.5
S=3cm

Next, the formula K=½ rs is used here to find k which is the area of a sector.
K=½(6)(3)
K=9cm²

So the answer is the arc length is 3cm and the area is 9cm².