CBSE Class 10th Areas of Sector and Segment of a Circle Details & Preparations Downloads

Class 10 Mathematics introduces an intriguing exploration into the realms of circles, focusing on 'Areas of Sector and Segment.' This topic not only broadens our understanding of circular geometry but also serves as a gateway to practical applications. Join us as we navigate the curves, angles, and areas that define this captivating chapter.

Unlocking Geometric Mastery CBSE NCERT Download Decodes 'Areas of Sector and Segment of a Circle' for Class 10

Segment of a Circle Definition

A segment of a circle can be defined as a region bounded by a chord and a corresponding arc lying between the chord’s endpoints. In other words, a circular segment is a region of a circle which is created by breaking apart from the rest of the circle through a secant or a chord. We can also define segments as the parts that are divided by the circle’s arc and connected through a chord by the endpoints of the arc. It is to be noted that the segments do not contain the center point.

Types of Segments in a Circle

According to the definition, the part of the circular region which is enclosed between a chord and corresponding arc is known as a segment of the circle. There are two classifications of segments in a circle, namely the major segment and the minor segment. The segment having a larger area is known as the major segment and the segment having a smaller area is known as the minor segment.

Area of a Segment of a Circle Formula

The formula to find segment area can be either in terms of radians or in terms of degree. The formulas for a circle’s segment are as follows:

Area of a Segment of a Circle Formula

Formula To Calculate Area of a Segment of a Circle
Area of a Segment in Radians	A = (½) × r² (θ – Sin θ)
Area of a Segment in Degrees	A = (½) × r ²× [(π/180) θ – sin θ]

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Theorems on Segment of a Circle

There are two main theorems based on a circle’s segments which are:

Alternate Segment Theorem
Angle in the Same Segment Theorem
Alternate Angle Theorem

I. Sector Area: Unraveling the Angular Measures

The blog commences with a deep dive into sector areas, emphasizing the relationship between central angles and the corresponding areas within a circle. Students grasp the concept that the area of a sector is proportional to its central angle, laying the foundation for more complex calculations.

II. Segment Area: The Space Between Chord and Arc

The exploration extends to circle segments, revealing the intricacies of the space enclosed between a chord and its corresponding arc. Students learn to calculate segment areas, embracing the challenge of dealing with diverse geometric elements within circular boundaries.

III. Formulas Demystified: Sector and Segment Calculations

The blog elucidates the formulas governing the computation of sector and segment areas, providing step-by-step guidance for students. Clear examples illustrate the application of these formulas, empowering learners to approach problems with confidence.

IV. Real-World Applications: Beyond the Classroom

The practical significance of understanding sector and segment areas comes to light. From calculating the areas of agricultural fields to designing circular stages for events, students explore how these geometric concepts manifest in real-world scenarios.

V. Problem-Solving Strategies: Navigating Complexities with Ease

The journey concludes with an emphasis on problem-solving strategies. Armed with a comprehensive understanding of sector and segment areas, students are equipped to tackle a variety of geometric challenges, enhancing their analytical and critical-thinking skills.

How to Calculate the Area of Segment of Circle?

if ∠AOB = θ (in degrees), then the area of the sector AOBC (A sector AOBC) is given by the formula;

(A sector AOBC) = θ/360° × πr2

Let the area of ΔAOB be AΔAOB. So, the area of the segment ABC(A segment ABC) is given by

(A segment ABC) = (A sector AOBC) – AΔAOB

(A segment ABC) = θ/360° × πr2 – AΔAOB

The area of ΔAOB can be calculated in two steps, As shown in fig. 2,

Calculate the height of ΔAOB i.e. OP using Pythagoras theorem as given below:

OP = √[r2–(AB/2)2] if the length of AB is given

or, OP = r cos (θ/2), if θ is given (in degrees)

CBSE Class 10th Downloadable Resources:

1. CBSE Class 10th Topic Wise Summary	View Page / Download
2. CBSE Class 10th NCERT Books	View Page / Download
3. CBSE Class 10th NCERT Solutions	View Page / Download
4. CBSE Class 10th Exemplar	View Page / Download
5. CBSE Class 10th Previous Year Papers	View Page / Download
6. CBSE Class 10th Sample Papers	View Page / Download
7. CBSE Class 10th Question Bank	View Page / Download
8. CBSE Class 10th Topic Wise Revision Notes	View Page / Download
9. CBSE Class 10th Last Minutes Preparation Resources (LMP)	View Page / Download
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11. CBSE Class 10th Formula Booklet	View Page / Download

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SAMPLE PRACTICE QUESTION

Q1: What is the area of a sector of a circle?
Ans: The area of a sector of a circle is the fraction of the circle enclosed by two radii and the corresponding arc. It is calculated using the formula \(A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2\), where \(\theta\) is the central angle, and \(r\) is the radius.

Q2: How is the central angle related to the area of a sector?
Ans: The central angle (\(\theta\)) determines the portion of the circle covered by the sector. The larger the central angle, the greater the area of the sector.

Q3: Can you provide an example of calculating the area of a sector?
Ans: Certainly! For a circle with a radius of 5 units and a central angle of 60 degrees, the area of the sector is \(\frac{60}{360} \times \pi \times 5^2\).

Q4: What is the area of a segment of a circle?
Ans: The area of a segment of a circle is the region enclosed by a chord and the arc it subtends. It is calculated by subtracting the area of the corresponding triangle from the area of the sector.

Q5: How is the central angle related to the area of a segment?
Ans: Similar to the sector, the central angle (\(\theta\)) influences the area of the segment. A larger central angle results in a larger area for the segment.