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 the NCERT Mathematics syllabus that deals with calculating areas of circles, sectors, segments, and related shapes using formulas and geometric properties.
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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. 3. Apply the formula:
$$ \text{Area of sector} = \frac{\theta}{360} \times \pi r^2 $$
Example:
If a circle has radius 7 cm and sector angle 60°, then
$$ \text{Area} = \frac{60}{360} \times \frac{22}{7} \times 7^2 = \frac{1}{6} \times 22 \times 7 = 25.67 \text{ cm}^2 $$
Finding the Area of a Segment of a Circle
A segment is the region between a chord and the corresponding arc. To find its area:
- Calculate the area of the sector formed by the chord and the center.
- Calculate the area of the triangle formed by the two radii and the chord.
- Subtract the triangle's area from the sector's area.
Formula:
$$ \text{Area of segment} = \text{Area of sector} - \text{Area of triangle} $$
Example:
If the radius $r=14$ cm and central angle $\theta=60^\circ$:
- Area of sector = $\frac{60}{360} \times \pi \times 14^2 = 153.94$ cm²
- Area of triangle = $\frac{1}{2} r^2 \sin \theta = \frac{1}{2} \times 14^2 \times \sin 60^\circ = 84.87$ cm²
Area of segment = $153.94 - 84.87 = 69.07$ cm²
Comparing Areas: Circle, Sector, and Segment
Understanding the differences between these areas helps solve problems quickly.
| Area Type | Definition | Formula |
|---|---|---|
| Circle | Entire area enclosed by the circle | $\pi r^2$ |
| Sector | Portion of circle defined by two radii and arc | $\frac{\theta}{360} \times \pi r^2$ |
| Segment | Area between chord and arc | Sector area − Triangle area |
Remember, the sector area depends on the angle $\theta$, while the segment area also depends on the chord length.
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.
How do you find the area of a sector in Class 10 Maths?
Use $\frac{\theta}{360} \times \pi r^2$, where $\theta$ is the sector angle in degrees.
What is the difference between a sector and a segment?
A sector is a 'slice' of a circle; a segment is the area between a chord and its arc.
Can I use $\pi = \frac{22}{7}$ for these calculations?
Yes, unless the question specifies otherwise, $\pi = \frac{22}{7}$ is commonly used.
Why is the chapter Areas Related to Circles important for Class 10 exams?
It covers key geometry concepts and formulas frequently tested in NCERT exams.
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