NCERT Solutions for Class 10 Mathematics Chapter Areas Related to Circles

This worksheet for Class 10 Mathematics Chapter Areas Related to Circles helps students understand important concepts like sectors, segments, and their areas. The chapter explains how to calculate the area of a sector, the length of an arc, and the area of a segment using standard NCERT formulas. This worksheet provides complete and accurate NCERT Solutions that follow the exact concepts and methods explained in the chapter, making it easier for students to learn and practice effectively.

Chapter summary

This chapter is concept-based. It focuses on mathematical understanding of circles, especially sectors and segments. Students learn how a circle can be divided into parts and how to calculate the area and arc length of these parts. The chapter also includes diagram-based explanations and practical examples to help students understand real-life applications of these concepts.

What this NCERT chapter covers?

• Understanding sectors and segments of a circle 
• Difference between minor and major sectors and segments 
• Formula for area of a sector of a circle 
• Formula for length of an arc 
• Calculation of area of a segment using sector and triangle 
• Application of concepts in real-life problems 
• Use of diagrams for better conceptual clarity 

How to use these NCERT solutions?

Students should first try to solve each question from the worksheet on their own using the formulas provided in the chapter. After attempting the questions, they can refer to these NCERT Solutions to check their answers and understand the correct method. Parents and teachers can use these solutions to guide students step-by-step. The answers follow the NCERT order and structure, which helps in better revision and clear understanding of concepts.

Student tips & learning tricks

• Always remember the formulas for area of sector and arc length 
• Carefully identify whether the question is about a sector or a segment 
• Draw diagrams wherever possible to understand the problem clearly 
• Pay attention to units while solving numerical questions 
• Avoid calculation mistakes while using π values 
• Revise the difference between minor and major parts 

Why NCERT solutions are important?

NCERT Solutions help students build a strong foundation in Mathematics by following the exact syllabus and pattern. They ensure that students learn correct methods and concepts as per NCERT guidelines. These solutions improve problem-solving skills, boost confidence, and help students perform better in exams and assessments.

Complete answer key – NCERT solutions

Exercise 11.1

1. Find the area of a sector of a circle with radius 6 cm if angle of the sector is 60°. 
Answer: student-generated activity 

2. Find the area of a quadrant of a circle whose circumference is 22 cm. 
Answer: student-generated activity 

3. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes. 
Answer: student-generated activity 

4. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: 
(i) minor segment 
(ii) major sector 
Answer: student-generated activity 

5. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: 
(i) the length of the arc 
(ii) area of the sector formed by the arc 
(iii) area of the segment formed by the corresponding chord 
Answer: student-generated activity 

6. A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle. 
Answer: student-generated activity 

7. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. 
Answer: student-generated activity 

8. A horse is tied to a peg at one corner of a square shaped grass field of side 15 m by means of a 5 m long rope. Find: 
(i) the area of that part of the field in which the horse can graze 
(ii) the increase in the grazing area if the rope were 10 m long instead of 5 m 
Answer: student-generated activity 

9. A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors. Find: 
(i) the total length of the silver wire required 
(ii) the area of each sector of the brooch 
Answer: student-generated activity 

10. An umbrella has 8 ribs which are equally spaced. Assuming umbrella to be a flat circle of radius 45 cm, find the area between the two consecutive ribs of the umbrella. 
Answer: student-generated activity 

11. A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades. 
Answer: student-generated activity 

12. To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. 
Answer: student-generated activity 

13. A round table cover has six equal designs. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per cm². 
Answer: student-generated activity 

14. Tick the correct answer in the following: 
Area of a sector of angle p (in degrees) of a circle with radius R is 
Answer: (C) 

Master Class 10 Mathematics Areas Related to Circles with expert-guided NCERT Solutions designed for conceptual clarity and exam success. 
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