What is Areas Related to Circles Class 10: Definition & Concepts
By ConceptScroll Team · Published on 19 June 2026 · 4 min read
What is Areas Related to Circles class 10? It is a chapter in NCERT Mathematics that deals with calculating areas of circles, sectors, segments, and related shapes. This topic is essential for Class 10 students to solve geometry problems efficiently.
Formulae for Areas and Circumference of Circles
The key formulas you must remember are:
| Shape | Formula | Variables |
|---|---|---|
| Circle Area | $A = \pi r^2$ | $r$ = radius |
| Circle Circumference | $C = 2 \pi r$ | $r$ = radius |
| Sector Area | $A = \frac{\theta}{360} \times \pi r^2$ | $\theta$ = angle in degrees |
| Segment Area | $A = $ Sector area $-$ Triangle area | Depends on $r$, $\theta$ |
Here $\pi$ is approximately 3.1416. These formulas help calculate the space inside circular shapes and their parts.
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How to Calculate the Area of a Sector
A sector is a portion of a circle enclosed by two radii and the arc between them. To find its area:
1. Identify the radius $r$ of the circle. 2. Find the central angle $\theta$ (in degrees) of the sector. 3. Use the formula:
$$ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 $$
Example: If a sector has radius 7 cm and central angle 60°, then
$$ \text{Area} = \frac{60}{360} \times \pi \times 7^2 = \frac{1}{6} \times 3.1416 \times 49 = 25.57 \text{ cm}^2 $$
Calculating the Area of a Segment of a Circle
A segment is the region between a chord and the corresponding arc of a circle. To find the area of a segment:
1. Calculate the area of the sector formed by the chord. 2. Calculate the area of the triangle formed by the two radii and the chord. 3. Subtract the triangle area from the sector area.
Formula:
$$ \text{Area of segment} = \text{Area of sector} - \text{Area of triangle} $$
Example: For a circle with radius 10 cm and central angle 60°:
- Sector area = $\frac{60}{360} \times \pi \times 10^2 = 87.96$ cm²
- Triangle area = $\frac{1}{2} \times 10 \times 10 \times \sin 60^\circ = 43.3$ cm²
So,
$$ \text{Segment area} = 87.96 - 43.3 = 44.66 \text{ cm}^2 $$
Comparing Areas: Circle, Sector, and Segment
Understanding the difference between these areas is important:
| Shape | Description | Area Formula |
|---|---|---|
| Circle | Full circle with radius $r$ | $\pi r^2$ |
| Sector | Part of circle defined by angle $\theta$ | $\frac{\theta}{360} \times \pi r^2$ |
| Segment | Area between chord and arc | Sector area $-$ Triangle area |
This comparison helps solve problems involving partial areas of circles.
Frequently asked questions
What is the formula for the area of a circle?
The area of a circle is $\pi r^2$, where $r$ is the radius of the circle.
How do you find the area of a sector in Class 10 Maths?
Use the formula $\frac{\theta}{360} \times \pi r^2$, where $\theta$ is the sector's central angle.
What is the difference between a sector and a segment?
A sector is the area enclosed by two radii and an arc; a segment is the area between a chord and its arc.
Why is the chapter Areas Related to Circles important for Class 10 exams?
It covers key geometry concepts and formulas essential for solving circle-related problems in NCERT exams.
Can the area of a segment be larger than the area of a sector?
No, the segment area is always less than the sector area since it excludes the triangle part.
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