Schooling · Class 10 · Mathematics · Areas Related to Circles · Chapter on a page
CBSE Class 10 · Mathematics · NCERT Mathematics
Areas Related to Circles: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
This note's current text has no applied fact-check on record.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- The circumference of a circle with…
- An arc is a part of the…
- The length of an arc subtending…
- The area of a sector with central…
- A chord divides a circle into two…
- Area of a segment = Area of the…
- For combined figures, identify which…
- Formulas and facts
- Circumference of circle
- Area of circle
- Length of arc
- Area of sector
- Area of segment
- Area of major sector
- Perimeter of sector
- Watch out for
- Confusing arc length with sector area
- Forgetting to subtract the…
- Using diameter instead of radius in…
- Mixing up minor and major sectors
- Not converting angle to degrees when…
What this chapter is about
This chapter extends your knowledge of circles from perimeter and area of a full circle to finding areas and perimeters of parts of circles. You learn to calculate the area of a sector (a slice of a circle, like a pizza slice) and the area of a segment (the region between a chord and its arc). These concepts connect your understanding of circles with central angles measured in degrees.
Key ideas
- The circumference of a circle with radius r is 2πr, and its area is πr².
- An arc is a part of the circumference; a sector is the region enclosed by two radii and the arc between them.
- The length of an arc subtending angle θ at the centre is (θ/360) × 2πr.
- The area of a sector with central angle θ is (θ/360) × πr².
- A chord divides a circle into two segments; the minor segment is the smaller region, the major segment is the larger.
- Area of a segment = Area of the corresponding sector − Area of the triangle formed by the two radii and the chord.
- For combined figures, identify which areas to add and which to subtract, then compute each part separately.
- Always use consistent units and substitute π = 22/7 or 3.14 as directed in the problem.
Formulas and facts to remember
- Quantity: Circumference of circle · Formula: 2πr · Meaning: Total length around the circle
- Quantity: Area of circle · Formula: πr² · Meaning: Region enclosed by the circle
- Quantity: Length of arc · Formula: (θ/360) × 2πr · Meaning: Part of circumference for angle θ degrees
- Quantity: Area of sector · Formula: (θ/360) × πr² · Meaning: Slice of circle for angle θ degrees
- Quantity: Area of segment · Formula: Area of sector − Area of triangle · Meaning: Region between a chord and its arc
- Quantity: Area of major sector · Formula: πr² − Area of minor sector · Meaning: Remaining part of circle
- Quantity: Perimeter of sector · Formula: 2r + arc length · Meaning: Two radii plus the curved part
Common mistakes
- Confusing arc length with sector area → Arc length is a distance (linear), sector area is a region (square units); use the correct formula for what is asked.
- Forgetting to subtract the triangle's area when finding a segment → A segment is smaller than the sector; always subtract the triangular part.
- Using diameter instead of radius in formulas → Check whether the problem gives radius or diameter; if diameter is given, divide by 2 before substituting.
- Mixing up minor and major sectors → Minor sector has the smaller angle (≤180°); major sector has the larger angle; their areas add up to πr².
- Not converting angle to degrees when needed → These formulas assume angle in degrees; if angle is in some other form, convert first.
Quick revision
- Arc length = (θ/360) × 2πr; sector area = (θ/360) × πr².
- Segment area = Sector area − Triangle area formed by the radii and chord.
- For combined figures, break into familiar shapes, find each area, then add or subtract.
- Major sector area + Minor sector area = Full circle area.
- Always check units and whether radius or diameter is given.