RD Sharma Class 10 Chapter 15 Solutions (Areas Related to Circles)
Our RD Sharma Class 10 Maths Solutions Chapter 15 – ‘Areas Related to Circles’ is compiled by our subject matter experts to help you prepare well for the CBSE Board exams. This is an important chapter from board exam point of view. In this chapter, you will learn about finding perimeters and areas related to circular figures in your daily lives. This chapter tells you that circles are divided into two specific parts known as sector and segment for the calculations. You will also learn about the underlying principles behind the calculation of the perimeter and area of a circle and the required formulas to do so. You are also taught how to determine areas of sector and segment of a circle applying different formulas and how to calculate areas of combined geometrical figures.
There are 4 exercises containing 52 questions in RD Sharma Class 10 Maths Solutions Chapter 15. The questions asked in this chapter are about determining the area and circumference of circles given when either the radius or diameter length is given. Some questions ask you to determine the length of arc or angle of arc subtended on the circumference of a circle. Other questions are based on the determination of the areas of major and minor segments given in a circle.
All of these questions have been answered precisely and in a step by step manner in our smart and systematic RD Sharma Class, 10 Maths Solutions Areas Related to Circles. The solutions are framed in such a way that they make the learning process engaging, interactive and efficient. They are easy to understand, and 100% accurate.
RD Sharma Class 10 Maths Areas Related to Circles: Important Topics
A lot of objects that we come across in day to day life are related to the circular shape, like wheels, dartboard, circular clock, drain cover, bangles, circular roads are some examples among others. So, it becomes important from the practical point of view to find perimeters and areas of circular figures. Class 10 Maths Areas Related to Circles deals with the methods of doing such measurements.
The concepts covered are discussed below.
- Perimeter and Area of a Circle
You learn here that perimeter, also known as circumference bears a constant ratio with its diameter which is denoted by the Greek letter π. And circumference is equal to 2 π r where r is the radius of the circle. We generally take the value of π as 22/7 or 3.14 approximately.
- Areas of Sector and Segment of a Circle
Here you will learn that the part of a circular area bounded by two radii and the corresponding arc is termed a sector of the circle and the portion of the circle surrounded between a chord and its corresponding arc is known as a segment of that circle. Next, you learn about minor and major sectors within a circle. Area of circle is equal to π r2.
Further, you will learn here that area of a sector of angle θ is equal to (θ/360) × π r2 and length of an arc of a sector of angle θ is given by (θ/360) × 2 π r.
- Areas of Combinations of Plane Figures
In this section of the chapter, you will learn how to calculate the areas of some combinations of plane figures which we usually come across in our daily lives. This is done by dividing the figure into appropriate geometrical figures like triangles, circles etc. and using the combinations to find the required area.
Area of the segment of a circle = Area of the corresponding sector – Area of the corresponding triangle.
RD Sharma Class 10 Maths Chapter 15: Exercise-Discussion
All the answers to 52 questions of 4 exercises of this chapter are drafted in a way such that they cover all the concepts learned in the chapter. The components of exercises from each exercise have been discussed below.
- There is a total of 19 questions in this exercise. Questions 1, 2, 4 ask you to find the circumference of the circle given.
- Question 3 asks you to determine the area of a circle when its circumference is given.
- Question 5 asks you to find the area of a circle whose radius is given.
- Question 6 uses your higher-order thinking skills to calculate the area of the circle.
- Question 7 uses your analytical skills to determine the diameter of the two given circles.
- Questions 9 and 10 ask you to determine the area of the quadrant of a circle by using your higher-order thinking skills.
- Questions 11 to 14 are application based on combined geometric figures questions asking you to find their areas.
- Question 15 to 19 are word problems that use your higher-order thinking skills and are based on the concepts learnt in this chapter.
This exercise consists of 20 questions. Question 1 asks you to determine the length of the arc subtended on the circumference, and question 2,5 asks to determine the angle subtended by arc on the circumference of given circles. Question 4 asks to determine the radius of the circle. Questions 6 and 7 ask you to determine the areas of sectors shown on the given circles. Question 8 asks you to determine the angle subtended by a sector when its area is given.
Question 10 to 14 ask you to determine the area of sector shown on a circle given with the value of some other parameters. Question 15, 16 uses your analytical skills in order to determine the area of a sector. Question 17 asks you to determine the radius of a circle. Question 18 is a composite question asking you to determine various parameters of the given circle. Questions 19 and 20 use your higher-order thinking skills where you are asked to prove certain equalities in case of geometric figures.
There is a total of 7 questions in this exercise. Questions 1 to 5 asks you to determine the area of minor and/or major segments of given circles where information about chord in the circles is given. Questions 6 and 7 are based on higher-order thinking skills and ask you to prove some trigonometric identities related to the segments of the given circles.
This exercise has a total of 6 questions, and all of them ask you to determine the area of either — one of the minor or major segments — or area of both the segments in the given circle. The questions are a bit complex and need your higher-order thinking skills to solve the same.
Benefits of RD Sharma Class 10 Maths Solutions for Chapter 15 – Areas Related to Circles
Some of the major benefits of referring to RD Sharma Solutions Class 10 Maths Solutions Chapter 15 – Areas Related to Circles are as follows.
- They help you build a strong conceptual foundation of the concepts and their implication in daily life problems.
- They are a handy study material for quick learning and revision during your Class 10 Board exams.
- They give you an elaborate idea of the types of questions asked in your board exams and the best ways to solve the same.
- They help you score well in your class 10 board exams by answering doubts and making the concepts clear.
- They have been devised to help you learn quickly and effectively. They help you become thorough with the chapter.