Math CentralQuandaries & Queries


Question from Amandsa, a student:

What is the formula for finding the sector of a circle?

Hi Amandsa,

If a sector has central angle that measures θ degrees then the sector is a fraction of the circle. The fraction is θ/360 since the central angle for the entire circle is 360 degrees.

The area of a circle of radius r is π r2 where π is approximately 3.1416. The area of a sector is a fraction of the area of the circle, in fact it's the same fraction as above so

area of a sector of a circle = θo/360o × π r2 square units.

The circumference of a circle of radius r is 2 π r so the length of the arc that of a sector with central angle θ is the same fraction of the circumference. Thus

the length of an arc of a circle with central angle θ = θo/360o × 2 π r units.




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