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Area Related to Circle – Comprehensive Notes
🔵 1. Introduction to Circle

A circle is a two-dimensional geometric figure where all points are at an equal distance from a fixed point called the centre.

🔑 Key Terms

Centre (O): Fixed point inside the circle

Radius (r): Distance from centre to any point on the circle

Diameter (d): Twice the radius → d = 2r

Circumference: Boundary of the circle

Chord: Line joining any two points on the circle

Arc: Part of the circumference

Sector: Region enclosed by two radii and an arc

Segment: Region enclosed by a chord and an arc

🔵 2. Value of π (Pi)

π ≈ 3.14 or 22/7

π = (Circumference ÷ Diameter)

🔵 3. Area of a Circle

📐 Formula:

Area of Circle
=
𝜋
𝑟
2
Area of Circle=πr
2

📌 Where r = radius

📝 Example:
If r = 7 cm

Area
=
22
7
×
7
×
7
=
154
cm
2
Area=
7
22
​

×7×7=154 cm
2
🔵 4. Circumference of a Circle

📐 Formula:

Circumference
=
2
𝜋
𝑟
Circumference=2πr
🔵 5. Area of Semicircle

📐 Formula:

Area
=
1
2
𝜋
𝑟
2
Area=
2
1
​

πr
2

📐 Perimeter of Semicircle:

𝜋
𝑟
+
2
𝑟
πr+2r
🔵 6. Area of Quadrant (¼ Circle)

📐 Formula:

Area
=
1
4
𝜋
𝑟
2
Area=
4
1
​

πr
2

📐 Perimeter:

𝜋
𝑟
2
+
2
𝑟
2
πr
​

+2r
🔵 7. Area of Sector of a Circle

📐 Formula:

Area of Sector
=
𝜃
360
°
×
𝜋
𝑟
2
Area of Sector=
360°
θ
​

×πr
2

📌 Where θ = angle at the centre

🔵 8. Length of Arc

📐 Formula:

Arc Length
=
𝜃
360
°
×
2
𝜋
𝑟
Arc Length=
360°
θ
​

×2πr
🔵 9. Area of Segment of a Circle

📐 Formula:

Area of Segment
=
Area of Sector
−
Area of Triangle
Area of Segment=Area of Sector−Area of Triangle
🔵 10. Area of Annulus (Ring)

📐 Formula:

Area
=
𝜋
(
𝑅
2
−
𝑟
2
)
Area=π(R
2
−r
2
)

📌 Where R = outer radius, r = inner radius

🔵 11. Important Applications

✔ Wheels
✔ Coins
✔ Plates
✔ Circular parks
✔ Clocks
✔ Pipes and rings

🧠 Exam Tips

✔ Always write units (cm², m²)
✔ Convert diameter to radius
✔ Use correct π value
✔ Draw neat diagrams


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