NCERT Exemplar Class 10 Maths Chapter 11 Solutions: Area Related to Circles
NCERT Exemplar Class 10 Maths Solutions for Chapter 11 ‘Area Related to Circles’ are created as an attempt to provide unhindered guidance in sorting all your doubts in one place. The topics covered in this chapter of NCERT Class 10 Maths Exemplar include the circumference of a circle, area of circles, the length of an arc with a given radius. The advanced level of mensuration topics has also been covered in this chapter such as areas of sectors and areas of segments in a given circle.
There are 60 questions collated in 4 exercises in the exemplar exercises for chapter 11. The exercises consist of multiple-choice questions, true or false exercises, short answer questions with reasoning besides the questions that are completely problem-based. The long answer type of questions includes complex math problems with figures to aid you to get clarity about the demand of the question.
You will be at ease with the answers provided to you by the expert team of Instasolv. The language used in the detailed step by step answers is very simple to understand. The answers at Instasolv are not just compliant to the exam pattern prescribed by CBSE but will also be compatible with your understanding of the subject.
Important Topics for NCERT Exemplar Class 10 Maths Solutions Chapter 11: Area Related to Circles
Introduction to Concepts Related to Circles
So far, we have been introduced to what is the area and circumference of a circle. In the previous classes, we have studied how a chord or angle subtended by an arc to the centre of the circle can form the sector and segment in a given circle. You will learn about major and minor sectors and the methods to calculate their areas in this chapter. Also, you will learn about the major and minor segments of the circle.
Circumference and Area of the Circle
- If we consider a circle with radius r, then Circumference of the circle = 2πr and area of the circle = πr2
- Consider two concentric circles with radii r1and r2 such that r1> r2 then, area=πr12–πr22= π(r12–r22)
Area and Length of Sectors and Segments
- Consider a sector with central angle θ and let the radius of the circle be r, then area of the sector = 360 θπr2/360, where θ is given in degrees.
- Consider a sector with central angle θ and let the radius of the circle be r, then length of the arc of the sector = 2πrθ/360
- Considering the circle with radius r, Area of the minor segment of the circle = area of the sector – the area of ∆ so formed.
- Area of the major sector of a circle of radius r = πr2 – an area of the minor sector so formed.
- Area of the major segment of a circle of radius r = πr2 – an area of the minor segment so formed.
Note: The value of π should always be taken as 22/7 unless stated in the question.
Exercise Discussion of NCERT Exemplar Class 10 Maths Solutions Chapter 11: Area Related to Circles
- Exercise 11.1 consists of MCQs covering objective type questions of the NTSE level. These questions will test your proficiency in applying the formula of segments and sectors.
- Exercise 11.2 consists of short answer type questions that will test reasoning skills. You will be required to check the validity of the given statements on the basis of your knowledge about the definitions of components of a circle.
- The third exercise 11.3 consists of short answer type, simple questions that can be directly solved using the formulae of circles.
- Exercise 11.4 comprises long answer type questions. To be able to solve these you are required to have absolute clarity in the topics of mensuration related to circles.
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