Sectors of Circles

K = area of the sector

r = radius

s = the arc length

Θ = the central angle always in radians


FORMULAS

K = ½r²Θ

K = ½rs

s = rΘ

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Ex.1:

The Sun is 93,000,000 miles away from the Earth on average. The diameter of the Sun is about 865,000 miles in diameter. What is its apparent size?
Identify what's given.
s = 865,000
Θ = ??
r = 93,000,000
s = rΘ
Plug into the formula.
865,000 = (93,000,000) Θ
Θ = .009301075
The suns apparent size is .009301075 radians

Ex.2:

A sector of a circle has arc length 10 cm and central angle 2.5 radians. Find its radius and area.
s = 11
Θ = 2.2
r = ??
You would use the formula to find the radius s = rΘ.
Plug into the formula and you get that r = 10/2.5= 4.
To find the area, you could use either K = ½r²Θ or K = ½rs .
K = ½(4²)2.5 = 20

r = 4 and K = 20