Arc length, sector area and segment area
Find the length of an arc of n°, the area of a circular sector and of a segment, with l = πRn/180 and S = πR²n/360.
- Ukraine: grade 9
- Russia: grade 9
Guide
In Ukrainian Grade 9 geometry (section 7) the circumference is C = 2πR. The whole circle is 360°, so an arc of 1° has length 2πR360 = πR180. An arc of n° has length l = πRn180. We take π ≈ 3.14.
A circular sector is the part of a disc between two radii. A disc splits into 360 equal sectors of 1°, each of area πR²/360. The sector holding an arc of n° has area S = πR²n360.
A circular segment is the part of a disc cut off by a chord AB. For a segment holding an arc smaller than 180°, subtract the area of triangle AOB from the sector: Sseg = Ssec − SAOB. Figures are drawn to scale: 1 cell is 1 cm.