Class 10 · Chapter 11

Areas Related to Circles

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

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Tip: open the NCERT PDF for the original chapter text alongside the notes here.

Detailed theory

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

3.14

Key concepts & formulas

Circumference

= 2\pi r

; Area

= \pi r^2

Arc length for angle

\theta

\dfrac{\theta}{360}\cdot 2\pi r

Sector area for angle

\theta

\dfrac{\theta}{360}\cdot \pi r^2

Segment area

=

Sector area

-

area of triangle.

Area of annular ring:

\pi(R^2 - r^2)

Use

\pi = 22/7

(rational) or

3.14

as needed.