Sector of Circles

Happy Easter Everyone!!

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




Example 1

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

or

K = ½(4)(10) = 20

Your answers would be r = 4 and K = 20




If a problem asks for apparent size, you should automatically assume to use the
formula s = rΘ where;

r = distance between two objects

Θ = apparent size

s = diameter of an object.




----Daniellee