Math CentralQuandaries & Queries


Question from Richard, a student:

please could you tell me the formula and answer to the following. I have a circle portion with a radius of 150mm and an angle of 120 deg. If an arc is drawn from one point to the other as the radii touch the circle circumference, i need to know the area of the segment and the formula to carry out the answer.
Many Thanks

Hi Richard,

The area of a circle of radius r is π r2. You have only a portion of the circle. Since all the way around the circle is 360 degrees the portion of the circle you have is 120/360 = 1/3. Since your sector is one-third of the circle it is one-third of the area. Hence the area is

1/3 π r2 = 1/3 × π × 1502 = 23561.9 square millimeters.


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