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NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related to Circles

Our NCERT Solutions for Class 10 Maths Chapter 12 – Areas Related To Circles are one of the best study materials for learning and revising during board exams. Our expert Maths teachers have formulated according to the present CBSE NCERT Class 10 Maths Book and CBSE Class 10 Maths Syllabus. They cover all important topics and sub-topics of the chapter such as area of a circle, circumference of a circle, the segment of a circle, a sector of a circle, the angle of a sector, area of a sector of a circle, area of a triangle and visualisations. This chapter comprises a total of 3 exercises. Our NCERT Solutions answer all questions of all exercises in a step by step manner.

The Chapter is related to Circles are well structured, a hundred percent accurate, to the point and easy to understand. We have streamlined new learning techniques to suit this tech-savvy generation and make learning a fun experience for them. They are just what you need to ace your board exams. Our NCERT Class 10 Maths Chapter 12 solutions help you in achieving full conceptual clarity and building a strong conceptual base.

Our comprehensive NCERT solutions cover a wide range of question types that are important from the board exam point of view. They follow a logical flow to help you learn faster, better and retain more. They have been drafted using the best methods of solving the problems. They also include detailed explanations, relevant examples and illustrative diagrams to help you learn efficiently.

CBSE NCERT Class 10 Maths Chapter 12

In NCERT Solutions for Chapter 12 – Areas Related To Circles, you will be focusing on how solid, and plane figures can be visualised. You shall also see how areas of the figures are derived. 

  • Introduction

In NCERT Class 10 Maths Chapter 12 – Areas Related To Circles, you will be learning about the area of a circle. The formula for which has been given below. 

Area of circle = πr2

where π=22/7 or 3.14

Here, the circle’s radius is r. 

π is considered to be the ratio of the circumference of a circle to its diameter. 

  • Circumference of a circle

In this section of the chapter, you will learn about a circle’s circumference, also called the perimeter of a circle. The formula of the same has been given below

Circumference of a circle= 2πr. 

  • The segment of a circle 

This portion of the chapter teaches you that a part of a circle which is separated and cut off with a chord or a secant from the main circle area in a circular portion is known as a segment of a circle. 

  • A Sector of a Circle:

This chapter teaches you that the section of a circle which is enclosed by two radii and an arc is termed as the circle’s sector or sector of a circle. The area which is larger in size is termed as the major sector, and the area which is smaller in size is termed as the minor sector.

  • The angle of a Sector 

Here you will learn that the angle which lies between the two radii is defined as the angle of a sector. 

  • Length of an arc of a sector

With the help of the angle of the sector and circumference of a circle, you can find the length of an arc of a sector. Our NCERT Solutions for Class 10 Maths Chapter 12-Areas related to circles will teach you to accurately do the same. 

Here, L (Length) = (θ/360°)×2πr

  • Area of a Sector of a Circle 

In Class 10 Maths Areas Related To Circles, Area of a sector is represented by (θ/360°)×πr2

Here, r is the radius and θ is the angle of this sector. 

The angle of the sector can either represent the major sector or the minor sector. It depends on various cases. 

  • Area of a Triangle 

This part of NCERT Solutions for Class 10th Maths Chapter 12 – Areas Related To Circles will make you understand how to find the area of a triangle. This is one of the simplest sections, where the area of a triangle will be calculated with the height and base. The formula for the same has been given below. 

Area = ½ x height x base 

The area of an equilateral triangle can be calculated with the formula given below.

Area = 3/4×a2  

Here, a is the side of the triangle

In the later part of Class 10 Maths Areas Related To Circles, you will be reading about the area of a segment of a circle, areas of different plane figures and areas of a combination of plane figures. 

NCERT CBSE Class 10 Chapter 12-Areas Related To Circles Exercise-Discussion

In NCERT CBSE Class 10 Maths Chapter 12, there are a total of 3 exercises. Below is a brief overview of the exercises. 

Exercise 12.1

This exercise of CBSE Class 10 Maths Syllabus, consists of 5 questions. Question 1 and question 2 are based on the radii of a circle. In these two questions, you will have to find the radius of the circle. Question 3 is a long answer question, in which you will have to find the area of each circle. Question 4 is a scenario-based question, in which you will have to find the number of revolutions that a car tyre has taken. Question 5 is based on the area of the circle and perimeter of a circle. 

Exercise 12.2

This exercise of NCERT CBSE Class 10 Maths Chapter 12, consists of 14 questions. This exercise majorly focuses on the area of a sector, area of a quadrant, minor segment, major segment and segment of the circle. Some questions of this exercise are short answer questions, and some are application-based questions that help you get thorough with this chapter.

Exercise 12.3

This exercise of NCERT Solutions for Class 10 Maths Chapter 12-Areas Related To Circles, consists of 16 questions. In this exercise, maximum questions are based on the diagrams. You have to look at the given figures properly and then and start solving according to the given data. Some types of questions asked in this exercise are finding the area of the shaded region or finding the area of the region, which is not shaded and application-based questions.