CBSE · Class 6-12

Class 10 · Mathematics (Standard)

Unit 11 · Class 10Mathematics (Standard)

Areas Related to Circles

Circumference and area of a circle, area of a sector and segment, combined figures.

Lessons

6 concepts

1
Basics of a Circle
For a circle of radius $r$ : circumference $C = 2\pi r$ , area $A = \pi r^2$ . Diameter $d = 2r$ . $\pi$ is the ratio $C/d$ and equals approximately $22/7$ or $3.14$ .
2
Sector of a Circle
The region bounded by two radii and the arc between them is a sector. If the angle at the centre is $\theta$ (in degrees), arc length $= \dfrac{\theta}{360}\cdot 2\pi r$ ; sector area $= \dfrac{\theta}{360}\cdot \pi r^2$ .…
3
Segment of a Circle
A segment is bounded by a chord and the arc it subtends. Minor segment area $=$ (sector area) $-$ (area of triangle formed by two radii and chord). Major segment area $=$ (circle area) $-$ (minor segment area).
4
Special Angles
Quarter circle: $\theta = 90^\circ$ → area $= \pi r^2/4$ . Semicircle: $\theta = 180^\circ$ → area $= \pi r^2/2$ . These simplify quickly and appear in many combined-figure problems.
5
Combined Figures
Areas made by combining circles with rectangles, triangles, or other polygons: add and subtract regions carefully. Look for symmetry to shortcut. Include units consistently (cm $^2$ , m $^2$ ).
6
Annular Ring
The area between two concentric circles of radii $R$ (outer) and $r$ (inner) is $\pi(R^2 - r^2)$ . This is useful for path around a circular garden, washer shapes, etc.

Skills to practise

Skill · medium

Areas Related to Circles — Practice