NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles (Ex 12.3)

The National Council of Educational Research and Training, or NCERT, is a distinct entity that was created in 1961 in accordance with the Societies Registration Act. It was founded by the Indian government as an organisation that would concentrate on the cultural, intellectual, and humanitarian advancement of the nation. NCERT will ensure that all students receive a common education. NCERT publishes academic textbooks and scholarly material for students from classes 1 to 12. As a result, NCERT books are required reading for all students. The NCERT syllabus offers a competitive edge at the national level after schooling and is not focused on recollection. The NCERT caters to the diversity of academic curricula in various regions of the country by publishing its content in various languages. The academic curriculum is designed to clarify and hone students’ understanding of theories, questions, and their comprehension of a wide range of subjects and themes.

For students in classes 1 to 12, the greatest study materials are the prescribed NCERT textbooks. These books are created by subject matter specialists after comprehensive study and analysis of a particular topic and after taking into account the cognitive abilities of students. NCERT textbooks are written in understandable terms and cover the essentials of every subject. The foundation of education in elementary, secondary, and senior secondary classes is defined by NCERT textbooks. Also, these NCERT textbooks will assist students in passing a variety of competitive tests after finishing school education, including the IIT JEE, NEET, UPSC, etc.

One of the core subjects for Class 10 students is Mathematics. It is essential for students to have a foundational understanding of Mathematics at the school level in order to improve their capacity to reason and think logically. Mathematical concepts can be used by students to solve difficulties in the real world. Every professional industry involves the application of the knowledge of Mathematics in some capacity. Students who are striving to pursue different professions can benefit from having a mathematical academic background. With the knowledge of its concepts, students can pursue careers in Astronomy, Astrophysics, Statistics, Weather Forecasting, and other related fields. One of the basic disciplines of the school education program, Mathematics is studied in schools starting in the first standard. The foundational concepts of mathematics are crucial for a student’s overall growth.

Every Class 10 student’s career path includes passing the Class 10 Board examination. This examination is an endeavour filled with expectations. The process of preparation is replete with complexities. If they are not properly supported and guided, some students may even experience a lack of confidence. A consistent schedule and well-written, well-researched study material can help a lot. The subject matter experts of Extramarks have undergonethe painstaking effort of compiling dependable study material. This relieves students of the perplexity of finding reliable digital reference materials. They have everything they need in NCERT Solutions to ace their upcoming test. This complex preparation can be made easy for them by using the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 and other reference materials created by Extramarks. By using the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 for Mathematics and other reference materials designed by Extramarks, students can make this difficult preparation easier. To constantly assess their level of preparation and work towards improving each time, students should solve past years’ papers. The kinds of questions posed by the Board can be better understood by using sample papers. This makes it easier to comprehend how much time should be allotted to solve each question during the examination.

The Extramarks website offers the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. These solutions contain all chapter exercises compiled into one source and are crafted by highly knowledgeable educators in compliance with the NCERT guidelines. Questions and solutions for Class 10 Maths Chapter 12.3 of the chapter Areas Related to Circles Exercise 12.3 to help students review the entire syllabus and achieve higher scores.

The topic of calculating the area of a combinatorial plane figure is covered in detail in the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 based on Areas Related to Circles. The idea of combinatorial figures will be used, for instance, if students have a square of paper and wish to cut out 4 circles, 2 on the bottom and 2 on the top. The area of a triangle, quadrilateral, and circle, as well as several related properties, are used in various calculations in this activity. Students are essentially asked to calculate the size of a shaded area that arises from the addition of a few known numbers. There are a total of 16 problems that are either intermediate or complex in the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. Students must employ both their cognitive and visualising skills if they want to be proficient in these calculations.

This assignment is largely concept-driven. Students must therefore have a strong foundation in the characteristics and components of various forms. It is suggested that, if they have any confusion regarding significant concepts, they should quickly review these topics with the aid of NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. The themes may appear complex at first glance, but with consistent practice, students will be able to solve them while learning the concepts.They can access the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 from the Extramarks website or mobile application.

The set of solutions compiled in the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 related to the chapter on Areas Related to Circles are comprehensive and  equipped with suitable examples. Students need to have a firm understanding of all the forms and properties of circles in order to solve these sums. In this exercise, appropriate diagrammatic illustrations are provided next to the questions. The right formulas should be applied, and the visuals should be understood by students. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 are curated to aid in thepreparation of the Class 10 board examination. In these solutions, every question is systematically solved.

Students will learn how to determine the distance between themselves and objects such as tablecloths, objects, curtains, etc with the aid of NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. The development of a student’s logic is a major focus of these exercises. A learner who completes this portion will be able to accurately answer any question about circles. So they must go through the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 thoroughly.

The NCERT Solutions for Class 10 Math Chapter 12 Exercise 12.3 fully answer all of the questions contained in Class 10 Math Exercise 12.3.Using a variety of strategies and a clear comprehension of concepts and reasoning, the mentors of Extramarks have prepared the 12.3 Class 10 Maths NCERT Solutions pertaining to the chapter Area Related to Circles. Students can clarify their concepts with the use of the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. Each question has a logical and exact solution in the 12.3 Class 10 Maths NCERT Solutions based on the chapter Areas Related to Circles. Students would find that NCERT Solutions are a great resource for helping them with their assignments, board preparation, and competitive test preparation.

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles (Ex 12.3) Exercise 12.3 

Having NCERT Solutions on hand has a lot of benefits. The solutions offered by Extramarks are organised by the exercises in each chapter, such as the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3, to prevent students from becoming confused. For Class 10 students who are dealing with a vast and diverse academic curriculum, the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 and other exercise solutions would undoubtedly make studying simpler. The proficient instructors at Extramarks have put their utmost effort and concentration into developing the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 and other NCERT Solutions. Students can use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 and other scholarly resources for review and doubt clarification. For the CBSE Class 10 board exams, NCERT textbooks and NCERT solutions are important resources. It aids in preparing students for the actual examination.

Students can get the PDF version of the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. To comprehend the ideas and questions in  Class 10 Maths Chapter 12 Exercise 12.3, students are recommended to use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 for a better understanding of the concepts.

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

Students can download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 curated by Extramarks from the link provided below.

NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles Exercise 12.3

Students are expected to carefully read through each chapter and comprehend the definitions of all the topics and subtopics. To prepare the chapters properly, it is imperative to comprehend the fundamentals of each chapter. The most effective method for learning the fundamentals of Mathematics is problem-solving. Before attempting the difficult questions, students should attempt the simple ones first. Effective board examination preparation is required of all students.

Before starting their study for the Mathematics examination, students must become familiar with the prescribed syllabus. The syllabus is required in order to plan a method for learning the chapters of mathematics.

For CBSE Class 10 board examinations, students should use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 for efficient preparation.It is emphasised that these solutions are the best resources for preparing for the mathematics exam.In Class 10 Maths Chapter 12.3, there are several complex exercises. Extramarks provides the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 in PDF format on their website and mobile application. Students can study the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 straight from the Extramarks website or mobile application, as well as download it at their convenience.

The problems and questions from the exercise are thoroughly solved in compliance with all CBSE regulations by subject matter experts at Extramarks. Students in Class 10 who are comprehensively familiar with all the concepts inculcated in the prescribed Mathematics textbook and have adequately practised all the exercises included in it can easily obtain the highest possible mark on the final examination. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 help students prepare for the final examination by providing the format of solutions that may be included in the examination from this chapter as well as the chapter’s significance in terms of topic weightage.

There are several exercises in this chapter that contain numerous questions in addition to those answered in NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. As previously noted, the in-house panel of subject experts have efficiently resolved or responded to all of these inquiries. Due to this, they are all guaranteed to be of the best quality, and students can use them to study for board exams. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 are essential to understanding all the concepts implicit in the textbooks and working through the exercises that are provided in order to attain excellence in the annual examinations.

Students should manage their time efficiently. To better prepare for the board exams, students are suggested to get the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. Students can download the solutions through the Extramarks educational website or Learning App. The most remarkable fact about the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 is that they can be used offline and online.

Here are some tips for using the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3

  • It is highly recommended that students becomefamiliar with the fundamental ideas embedded in themes like circles, squares, rectangles, triangles, etc. before beginning this chapter.
  • From the NCERT Class 10 books, students are advised to read and retain significant formulas relating to sectors and segments.
  • To grasp the strategy for completing the questions, students are advised to read through the examples provided in the textbook and the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3.

To find the right response or learn how to answer a certain question, students can use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 while practising.

NCERT Solutions for Class 10 Maths Chapter 12 Exercises

The themes of a circle’s perimeter and area are presented in the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3. By incorporating various concepts and formulas related to the areas and perimeter of a circle and its sections, the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 proceeds to describe how to determine the sector and segment areas of circular regions. Additionally, students will be able to understand how to determine the areas of specific combinations of planar figures that include circles. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 include solved questions about the area of a circle and other kinds of questions associated with the circular region.

The area and perimeters of circles, segments, and sectors are all covered under the chapter titled “Area Related to Circles,”. Chapter 12 of the Mathematics textbook on Areas Related to Circles discusses the perimeter and area of a circle as well as calculating the areas of two distinct regions known as the sector and segment. The theme of Mensuration also includes areas that pertain to circles. Along with the radii of a circle, this topic also discusses the sectors and their angles. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 will assist students in understanding the aforementioned concepts easily.

A circle’s area is the area that it takes up in the 2D plane. It is used to figure out how much space a circular field occupies. Half of a circle’s circumference and diameter add up to a semicircle perimeter. Between two radii and a neighbouring arc are the sectors. The area and perimeter of a circle are covered in further detail in Chapter 12 of the prescribed textbook of Mathematics for Class 10. Formulas related to the areas and perimeters of a circle are used to determine results like the radii of the circle that encompass the combined area or perimeter covered by two additional circles, to determine the area of rings, and to determine the distance travelled during specific revolutions.

Sector and circle segment areas:

The sector of the circle is the portion of the circle formed by the two radii and the associated arc. The segment of the circle is the portion of the circle that is between the chord and its matching arc. A big segment and a smaller segment make up the segment. Major and minor sectors are used to categorise the sectors. The area and perimeter are influenced by the angle that the central arc occupies.

Area of figural combinations:

This theme deals with calculating the surface areas of several plane figures and polygons used in different designs.

Sector’s inclination:

The angle that is contained between two radii is known as the sector angle.

The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 containdescriptive details about all the topics necessary to understand the concepts described above. Undoubtedly, these concepts are challenging to grasp. Hence, the Extramarks website has engineered the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3, which are compiled with all simplified terminologies and step-wise solutions to questions. Thus, these solutions would provide comprehensive explanations to enable students to learn quickly. To download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3, students must visit the Extramarks e-learning portal. Besides these learning resources, Extramarks also provides NCERT Solutions for grades 1 to 12 on its website.

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Q.1 Find the area of the shaded region in the following figure, if PQ = 24 cm, PR = 7 cm and O is the centre of the circle.


Ans

In the given figure, RQ is diameter. Therefore, ∠RPQ=90°By applying Pythagoras Theorem in ΔPQR, we get        QR2=PQ2+PR2=242+72=625or QR=625=25 Therefore, radius of the circle=OR=QR2=252Area of the semi-circle RPQOR=12πr2=12×227×(252)2=687528 cm2Area of ΔPQR=12×PQ×PR=12×24×7=84 cm2Area of the shaded region =Area of semi-circle RPQOR−Area of ΔPQR  =687528−84=452328 cm2

 

Q.2

Find the area of the shaded region in the followingfigure, if radii of the two concentric circles withcentre O are 7 cm and 14 cm respectively and∠AOC=40°.

Ans

Radius of inner circle=7 cmRadius of outer circle=14 cmArea of the shaded region =Area of sector OAFC−Area of sector OBED              =40°360°×π(14)2−40°360°×π(7)2              =19×227×196−19×227×49              =6169−1549              =4629              =1543 cm2

 

Q.3 Find the area of the shaded region in the following figure, if ABCD is a square of side 14 cm and APD and BPC are semicircles.


Ans

Radius of each semicircle=7 cmArea of each semicircle=12πr2=12×227×7×7=77 cm2Area of square ABCD=(side)2=142=196 cm2Area of shaded region                   =Area of square ABCD−Area of the two semicircles                   =196−2×77=42 cm2

 

Q.4 Find the area of the shaded region in the following figure, where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.


Ans

Area of the circle=πr2=227×62=227×36=7927 cm2Area of the sector=60°360°×227×62=79242 cm2=1327 cm2Area of the given equilateral triangle=34(side)2                                                                               =34×122                                                                               =363 cm2Area of the shaded region=Area of the circle+Area of the triangle    −Area of the sector =7927+363−1327=(6607+363) cm2

 

Q.5 From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the following figure. Find the area of the remaining portion of the square.


Ans

Area of the square ABCD=(side)2=42=16 cm2Area of each sector=90°360°×227×12=1114 cm2Area of the circle=πr2=227×12=227 cm2Area of the shaded region=Area of the square ABCD −Area of the circle −4×Area of the sector =16−227−4×1114=687 cm2

 

Q.6 In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in the following figure. Find the area of the design (shaded region).


Ans

 

Radius of the circle=32 cmAD is the median of the triangle ABC.         AO=23AD=32or   AD=48 cmIn Δ ABD,          AB2=AD2+BD2=482+(AB2)2or   AB=323 cmArea of equilateral Δ ABC=34(side)2=34(323)2=7683 cm2Area of the circle=πr2=227×(32)2=225287 cm2Area of the design=Area of the circle−Area of  Δ ABC =(225287−7683) cm2

 

Q.7 In the following figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region.


Ans

Area of the square ABCD=(side)2=142=196 cm2Distance between two centres of circles=AB=14 cmRadius of each circle=AB2=142=7 cmArea of each sector=90°360°×227×72=772 cm2Area of the shaded region=Area of the square ABCD −4×Area of the sector =196−4×772=42 cm2

 

Q.8 The following figure depicts a racing track whose left and right ends are semicircular.

The distance between the two inner parallel line segments is 60 m and they are each 106 m long. If the track is 10 m wide, find:

  1. the distance around the track along its inner edge
  2. the area of the track.

Ans

Distance around the track along its inner edge                       =AB+arc BEC+CD+arc DFA =106+12×2πr+106+12×2πr=28047 mArea of track =area of rectangle GHIJ−area of rectangle ABCD  +area of semicircle HKI−area of semicircle BEC +area of semicircle GLJ−area of semicircle AFD =106×80−106×60+12×227×(40)2−12×227×(30)2        +12×227×(40)2−12×227×(30)2   =4320 m2

 

Q.9 In the following figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.


Ans

Area of smaller circle=πr2=227×72×72=772 cm2Area of a quadrant of the bigger circle =14π (7)2=14×227×(7)2=772 cm2Area of triangle OBC =12×7×7=492cm2Area of a shaded segment of the bigger circle =Area of a quadrant−Area of triangle OBC =772 −492=282= 14 cm2Total area of the shaded region =Area of smaller circle+2Area of a shaded segment = 772 +2×14=1332=66.5 cm2

 

Q.10

The area of an equilateral triangle ABC is 17320.5 cm2. With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the sideof the triangle (see the following figure). Find thearea of the shaded region. (Use π=3.14 and 3=1.73205)

Ans

Let side of equilateral triangle be a.    Area of equilateral triangle=17320.5 cm2or                               34a2=17320.5or                                    a2=4×17320.53or                                    a=200 cmEach sector is of 60°.So area of sector ADEF=60°360°πr2=16×3.14×(100)2                                                  =157003Area of shaded region=Area of equilateral triangle                                                      −3×area of each sector                                               =17320.5−3×157003                                               =1620.5 cm2

 

Q.11 On a square handkerchief, nine circular designs each of radius 7 cm are made (see the following figure). Find the area of the remaining portion of the handkerchief.


Ans

Side of the square=42 cm∴ Area of square=1764 cm2Area of each circle=227×72=154 cm2Area of 9 circles=9×154=1386 cm2Required area=1764 −1386=378 cm2

 

Q.12 In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) quadrant OACB, (ii) shaded region.


Ans

Given that, r=3.5 cm and OD=2 cmArea of the quadrant OACB=90°360°×227×(3.5)2=778 cm2Area of Δ OBD=12×OB×OD=12×3.5×2=3.5 cm2Area of shaded region=Area of the quadrant OACB                                                      −Area of Δ OBD                                               =778−3.5=498 cm2

 

Q.13 In the following figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)


Ans

Given that, OA=20 cmArea of square OABC=202=400 cm2Radius of the quadrant  OPBQ=Diagonal of the square OABC                                                                =202 cmArea of the quadrant OPBQ=90°360°×3.14×2022                                                            =628 cm2Area of shaded region=Area of the quadrant OPBQ                                                      −Area of square OABC                                               =628−400=228 cm2

 

Q.14 AB and CD are respectively arcs of two concentric circles of radii 21 cm and 7 cm and centre O (see the following figure). If ∠AOB = 30°, find the area of the shaded region


Ans

Area of shaded region=Area of the sector ABO                                                      −Area of the sector CDO                                               =30°360°×227×(21)2−30°360°×227×(7)2                                               =3083 cm2

 

Q.15 In the following figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region.


Ans

Area of shaded region               =Area of the semicircle+Area of ΔABC                      −Area of the quadrant ABC               =12×227×142+14222+12×142−90°360°×227×142    =154+98−154               =98 cm2

 

Q.16 Calculate the area of the designed region in the following figure common between the two quadrants of circles of radius 8 cm each.


Ans

The designed area is the common region between two equal sectors BAEC and DAFC.Area of the sector BAEC=Area of the sector DAFC =90°360°×227×(8)2=3527 cm2Area of ΔADC=Area of ΔABC=12×8×8=32 cm2Area of the designed portion =2×(Area of segment AEC) =2×(Area of sector BAEC−Area of ΔABC) =2×(3527−32)=2567 cm2

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FAQs (Frequently Asked Questions)

1. Are the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 quintessential for the preparation for the Class 10 board examination?

Yes, the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 are a quintessential learning asset for the preparation for the Class 10 board examination. Students should take reference from this quality learning resource because the solutions provide an accurate and concise form of response to various kinds of questions. These solutions will be helpful while revising the entire chapter. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 contain short keywords that would help in recalling the major concept quickly. It is also a time-saving tool.

2. Which of the questions in Class 10 Maths Chapter 12 Exercise 12.3 are important?

Each question is significant in its own way. The more difficult ones provide a strengthened understanding of the application of concepts while the simpler ones would help enhance efficiency. For a better understanding of the chapter’s contents and to perform well on examinations, all the questions must thus be given equal importance. For additional information on the resources available for each chapter, students are advised to access the Extramarks website. Students can also carefully peruse the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.3 for preparation for the Mathematics examination.

3. How many chapters are there in the prescribed NCERT textbook of Mathematics of Class 10?

There are 15 chapters in total in the prescribed textbook of Mathematics for Class 10. These chapters can be listed as follows-

Chapter-1 Real Number

Chapter-2 Polynomials

Chapter-3 Pair Of Linear Equations In Two Variables

Chapter-4 Quadratic Equation

Chapter-5 Arithmetic Progression

Chapter-6 Triangles

Chapter-7 Coordinate Geometry

Chapter-8 Trigonometry

Chapter-9 Applications Of Trigonometry

Chapter-10 Circles

Chapter-11 Constructions

Chapter-12 Areas Related To Circles

Chapter-13 Surface Areas And Volumes

Chapter-14 Statistics

Chapter-15 Probability