Sector of a circle
- CBSE · NCERT Class 10, Ch 11 Areas Related to Circles
A sector is the part of a circle enclosed by two radii and the arc between them, shaped like a slice of pizza.
Two radii split a circle into two sectors. The smaller one is the minor sector and the larger one is the major sector. The angle between the radii at the centre decides the size. A sector with angle θ is θ/360 of the whole circle. So its area is (θ/360) × πr².
A small example
A circle has radius 7 cm, and a sector has angle 90°. Its area is 90/360 × 22/7 × 7 × 7 = 1/4 × 154 = 38.5 cm². The whole circle is 154 cm². So the major sector is 154 − 38.5 = 115.5 cm².
Where marks go
Question 36 of CBSE's 2026-27 Maths Basic sample paper is a case study about a paper fan shaped like a sector. The angle at the centre is 60°. Part (i) asks for the area of one face of the fan. Part (ii) asks for the area of a strip between two radii of 4 cm and 10 cm.
Each part is worth 1 mark. The 2026-27 Maths Basic marking scheme splits each one into two halves. Even a 1-mark part rewards the working. For a 2-mark sector question split three ways, see step marking.
Sources
Facts last checked against these sources on 30 September 2026.
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