Knowledge organisers

Areas Related to Circles: CBSE Class 10 Maths knowledge organiser

Everything to know about areas related to circles on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Sector: The region between two radii and an arc.
Segment: The region between a chord and its arc.
Minor and major: The minor sector or segment is the smaller one; the major is the larger one.

Key formulas

Circle	\(C=2\pi r,\) \(A=\pi r^2\)
Arc length; sector area (angle \(\theta\))	\(l=\frac\theta{360^\circ}\times2\pi r,\) \(A=\frac\theta{360^\circ}\times\pi r^2\)
Segment	\(\text{area}=\text{sector}-\tfrac12r^2\sin\theta\)
Segment, \(\theta=60^\circ,90^\circ,120^\circ\): subtract \(\tfrac{\sqrt3}4r^2\), \(\tfrac12r^2\), \(\tfrac{\sqrt3}4r^2\)
Perimeter of sector; ring	\(2r+l;\) \(\pi(R^2-r^2)\)
Minute hand sweeps \(6^\circ\) per minute; hour hand \(0.5^\circ\) per minute

Worked example

Find the area of a sector of angle \(40^\circ\) in a circle of radius 21 cm \(\left(\pi=\frac{22}{7}\right)\).

\(\dfrac{40}{360}\times\dfrac{22}{7}\times441=\dfrac19\times1386=154\ \text{cm}^2\).

Common mistakes

Adding the triangle to the sector instead of subtracting it to get the minor segment.
Using the diameter in place of the radius.
Forgetting the two radii when finding the perimeter of a sector.
Using \(\pi=3.14\) when the question says \(\frac{22}{7}\), or rounding too early.

You should be able to…

Find the length of an arc and the area of a sector for any angle.
Find segment areas for 60°, 90° and 120°, and solve clock-hand and sector-perimeter questions.
Write complete long answers on shaded regions, combining sectors, triangles and squares without missing a piece.
Work backwards from a given area or perimeter to the radius or angle, and handle major segments.

The printable sheet

Areas Related to Circles knowledge organiser for CBSE Class 10 Maths: one A4 page of key definitions, formulas, a worked example and common mistakes — Areas Related to Circles knowledge organiser (CBSE Class 10 Maths), A4. Download the PDF.

Revise it next

Other CBSE Class 10 Maths topics: Real Numbers · Polynomials · Pair of Linear Equations in Two Variables · Quadratic Equations · Arithmetic Progressions · Triangles · Coordinate Geometry · Introduction to Trigonometry · Some Applications of Trigonometry · Circles · Surface Areas and Volumes · Statistics · Probability · All CBSE Class 10 Maths organisers