case study questions areas related to circles

Class 10 Maths Case Study Questions Chapter 12 Areas Related to Circles

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Case study Questions in the Class 10 Mathematics Chapter 12  are very important to solve for your exam. Class 10 Maths Chapter 12 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving Class 10 Maths Case Study Questions Chapter 12  Areas Related to Circles

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In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

Areas Related to Circles Case Study Questions With Answers

Here, we have provided case-based/passage-based questions for Class 10 Maths  Chapter 12 Areas Related to Circles

Case Study/Passage-Based Questions

Question 1:

(a) 700 cm

(b) 729 cm

(c) 732 cm

(d) 735 cm

Answer: (b) 729 cm2

(ii) Area of rectangle left for car parking is

(a) 64 cm

(b) 76 cm

(c) 81 cm

(d) 100 cm

Answer: (c) 81 cm2

(iii) Radius of semi-circle is

(a) 6.75 cm

(b) 7 cm

(c) 7.75 cm

(d) 8.75 cm

Answer: (a) 6.75 cm

(iv) Area of a semi-circle is

(a) 61.59 cm

(b) 66.29 cm

(c) 70.36 cm

(d) 71.59 cm

Answer: (d) 71.59 cm2

(v) Find the area of the shaded region

(a) 660.82 cm

(b) 666.82 cm

(c) 669.89 cm

(d) 700 cm

Answer: (b) 666.82 cm2

Question 2:

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A:  Brooch A is made with silver wire in the form of a circle with a diameter of 28mm. The wire is used for making 4 diameters which divides the circle into 8 equal parts.

Design B:  Brooch b is made of two colors – Gold and silver. The outer part is made of Gold. The circumference of the silver part is 44mm and the gold part is 3mm wide everywhere.

Refer to Design A

1. The total length of silver wire required is

Answer: b) 200 mm

2. The area of each sector of the brooch is

Answer: c) 77 mm2

Refer to Design B

3. The circumference of outer part (golden) is

a) 48.49 mm

c) 72.50 mm

d) 62.86 mm

Answer: d) 62.86 mm

4. The difference of areas of golden and silver parts is

a) 18  π

b) 44  π

c) 51  π

d) 64  π

Answer: c) 51 π

5. A boy is playing with brooch B. He makes revolution with it along its edge. How many complete revolutions must it take to cover 80 mm?

Answer: c) 4

Hope the information shed above regarding Case Study and Passage Based Questions for Class 10 Maths Chapter 12 Areas Related to Circles with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Class 10 Maths Areas Related to Circles Case Study and Passage-Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team Study Rate

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CBSE Case Study Questions for Class 10 Maths Area Related to Circles Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Area Related to Circles  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

MCQ Set 1 -

Mcq set 2 -, checkout our case study questions for other chapters.

• Chapter 10: Circles Case Study Questions
• Chapter 11: Construction Case Study Questions
• Chapter 13: Surface Area and Volumes Case Study Questions
• Chapter 14: Statistics Case Study Questions

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Sit through chapter wise FULLY INVIGILATED TESTS

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CBSE Class 10 Maths Case Study Questions for Chapter 10 - Circles (Published By CBSE)

Check cbse class 10 maths case study questions for chapter 10 - circles. these questions have been published by the board for class 10 mathematics..

CBSE: Case study questions for CBSE Class 10 Maths Chapter 10 - Circles are provided here which students can practice to get familiarised with the new format of questions. These questions have been published by CBSE itself. Answers to all the questions have been provided for the convenience of students. Case study questions are helpful for the preparation of the Class 10 Maths Exam 2021-2022.

Case Study Questions for Class 10 Maths Chapter 10 - Circles

CASE STUDY 1:

A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity.

After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.

1. In the given figure find ∠ROQ

Answer: c) 150

2. Find ∠RQP

Answer: a) 75

3. Find ∠RSQ

Answer: b) 75

4. Find ∠ORP

Answer: a) 90

CASE STUDY 2:

Varun has been selected by his School to design logo for Sports Day T-shirts for students and staff . The logo design is as given in the figure and he is working on the fonts and different colours according to the theme. In given figure, a circle with centre O is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. The lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively.

1. Find the length of AD

Answer: a) 7

2. Find the Length of BE

Answer: b) 5

3. Find the length of CF

Answer: d) 3

4. If radius of the circle is 4cm, Find the area of ∆OAB

Answer: c) 24

5. Find area of ∆ABC

Answer: b) 60

Also Check:

Tips to Solve Case Study Based Questions Accurately

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CBSE 10th Standard Maths Subject Areas Related to Circles Case Study Questions With Solution 2021

CBSE 10th Standard Maths Subject Areas Related to Circles Case Study Questions With Solution 2021 QB365 - Question Bank Software May-22 , 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

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Final Semester - June 2015

Case Study Questions

(ii) Find the area of the red region.

(iii) Find the radius of the circle formed by combining the red and silver region.

(iv) Find the area of the silver region.

(v) Area of the circular path formed by two concentric circles of radii r 1  and r 2  (r 1 > r 2 ) =

(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units
(\({r}_{1}^{2}\) + \({r}_{2}^{2}\)) sq. units	(\({r}_{1}^{2}\) - \({r}_{2}^{2}\)) sq. units

(ii) Area of rectangle left for car parking is

(iii) Radius of semi-circle is

(iv) Area of a semi-circle is

(v) Find the area of the shaded region

(ii) Area of quadrant BCD is

(iii) Find the area of \(\Delta\) CEF.

(iv) Area of the shaded portion is

(v) Area of the unshaded portion is

(ii) Area of the region grazed by the cow is

\((a) \frac{\angle A}{360^{\circ}} \times \pi \times(3.5)^{2}\)

\((b) \frac{\angle B}{360^{\circ}} \times \pi \times(24)^{2}\)

\((c) \frac{\angle C}{360^{\circ}} \times \pi \times(3.5)^{2}\)

(iii) Area of region grazed by the buffalo and the horse is

\((a) \frac{(\angle A+\angle C)}{360^{\circ}} \times \pi \times(5.5)^{2}\)	\((b) \frac{(\angle B+\angle C)}{360^{\circ}} \times \pi \times(5.6)^{2}\)
\((c) \frac{(\angle A+\angle C)}{360^{\circ}} \times \pi \times(3.5)^{2}\)	\((d) \frac{(\angle B+\angle C)}{360^{\circ}} \times \pi \times(3.5)^{2}\)

(iv) Total area grazed by the cow, the buffalo and the horse is

(v) Find the area of the field that cannot be grazed.

(ii) Find the area of the circle.

(Hi) If D lies at the middle of arc BC, then area of region COD is

(iv) Area of the \(\Delta\) BAC is

(v) Find .the area of the polluted region.

*****************************************

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CBSE Class 10 Maths 2024-25: Chapter 11 Areas Related to Circle Competency-Based Questions with Answers; Download Free PDF

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As the CBSE Class 10 board exams  get closer, students need to understand the new  exam pattern . Starting in the  2024-25 school year , CBSE will include  50% more competency-based questions . These questions will be both  multiple choice  and  written , focusing on how to use what students have learned in  real-life situations .

This article explores  Chapter 11 Areas Related to Circle . It highlights key  competency-based questions  and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 11 Areas Related to Circle

Competency-based questions  are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as  case studies ,  true-false questions ,  gap-filling tasks , and  long or short answer questions .

Competency-based questions in  Chapter 11: Areas Related to Circle   go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 11: Areas Related to Circle Important Competency-Based Questions

Multiple choice questions.

Answer. (3)

Answer. (2)

1. 135° 2. 200° 3. 225° 4. (cannot be determined as the radius of circle is not given)

Answer. (4)

Answer. (1)

Q.6 A circular pond needs to be fenced along its circumference. One-fourth of the fencing is already done, which cost Rs 750 at the rate of Rs 50 per metre. How many metres of the pond still need to be fenced?

1. 15 2. 20 3. 45 4. 60

Q.7 Which of the following information is NOT sufficient to differentiate between minor and major sector of a circle?

1. the angle subtended at the centre 2. the radius of the circle 3. the area of the sector 4. the length of the arc

Free Response Questions

Q.8 In a circular agricultural field, a sector subtending an angle of 120° at the centre is dedicated to growing sugarcane.

If the radius of the circular field is 30 meters, what is the area of the land used for growing sugarcane? Show your work.

(Note: Take π as 3.14.)

Q.9 Anjali got the following question in her class test.

"A 13 cm chord of a circle subtends an angle of 60° at the centre. Find the area of the minor segment."

After the test, she went to the teacher and said, "The question cannot be answered as it doesn't mention the radius of the circle".

Is Anjali right or wrong? Give a valid reason for your answer.

Answer.  Writes that Anjali is wrong and gives a reason. For example, since the chord extends an angle of 60° at the centre, it forms an equilateral triangle with the radii and hence, the radius is 13 cm.

294π × 6 = 1764π cm 2

(Award full marks if radius is calculated first and then the area of the circle.)

Q.12 The length of an arc of a circle is 22 cm and its radius is 21 cm.

Answer the questions based on the given information. An archery target board consists of three concentric circles with centre O as shown below. The innermost circle has a radius of 7 cm, the middle circle has a radius of 14 cm, and the outer circle has a radius of 28 cm. The target board is divided into four equal parts by AC and BD, which are the diameters of the outermost circles. The scoring system for the game is as follows: Area LIO: 10 points Area KJIEFG: 7 points Area ABEH: 4 points

Q.14 If the target lands on the boundary of the 4 points scoring area, a deduction of 1 point occurs, resulting in a score of 3 points. Find the length of the boundary in which 3 points can be scored. Show your work.

Q.15 Find the area KJIEFG. Show your work.

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Chapter 11 Class 10 Areas related to Circles

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Updated for new NCERT - 2023-2024 Boards.

NCERT Solutions of all exercise questions and examples of Chapter 11 Class 10 Areas related to Circle. Answers to all questions are available with video free at teachoo.

In this chapter, we will

• Revise our concepts about Area and Perimeter of Circle , and do some questions
• Then, we will see what arc , sector and segment of a circle is
• We will learn the formula for length of an arc
• and Area of sector
• Then, using Area of sector and Area of triangle formulas, we find Area of Segment
• We do some questions where different figures are combined, and we need to find their area and perimeter

Click on an exercise link below to learn from the NCERT Book way.

Or you can also learn from Teachoo way, click on any concept below Concept Wise to get started.

In concept wise, the chapter is divided into concepts. First the concept is taught, and then we solve the questions related to the concept. All questions are ordered easy to difficult. That means, easiest question is in the beginning and the more difficult question is at the end.

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Serial order wise

Concept wise.

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• Case Study Class 10...

Case Study Class 10 Maths Questions

Table of Contents

myCBSEguide App

Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

I	NUMBER SYSTEMS	06
II	ALGEBRA	20
III	COORDINATE GEOMETRY	06
IV	GEOMETRY	15
V	TRIGONOMETRY	12
V	MENSURATION	10
VI	STATISTICS & PROBABILITY	11

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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• Class 10 Maths Basic Sample Paper 2024
• How to Revise CBSE Class 10 Maths in 3 Days
• CBSE Practice Papers 2023
• Class 10 Maths Sample Papers 2024
• Competency Based Learning in CBSE Schools

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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• Important Questions
• Previous Years Questions
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• Assertion and Reason Questions

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Areas Related to Circles Questions

Areas Related to Circles Questions with answers are provided here. Class 10 students can practise the questions based on areas related to circles to prepare for the exams. These areas related to circles problems are prepared by our subject experts as per the latest exam pattern. All the materials here are formulated according to the NCERT curriculum and latest CBSE syllabus (2022-2023). Learn more: Areas Related to Circles Class 10 Notes .

Formulas of Areas Related to Circles:

Area of circle = πr 2

• Circumference of circle = 2πr
• Length of an arc of a sector = L= (θ/360°)×2πr
• Area of a sector of circle = (θ/360°)×πr 2

Areas Related to Circles Questions and Solutions

Q.1: If the radius of a circle is 4.2 cm, find its area.

Solution: Given,

Radius of circle = 4.2 cm

By the formula, we have;

A = π(4.2) 2

A = 55.44 cm 2

Q.2: If the area of a circle is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, calculate the diameter of the larger circle.

Diameter of a circle, d 1 = 10 cm

Radius, r 1 = 10/2 = 5cm

diameter of another circle, d 2 = 24 cm

Radius, r 2 = 24/2 = 12cm

According to the question;

Area of a circle = area of circle 1 + area of a circle 2

πR 2 = πr 1 2 + πr 2 2

πR 2 = π(r 1 2 + πr 2 2 )

R 2 = 5 2 + 12 2 = 25 + 144

R 2 = 169 = 13 cm

Therefore, required diameter = 2(13) = 26 cm

Q.3: The circumference of a circular field is 528 m, find the radius of the field.

Circumference = 528 m

R = (528 x 7)/(2 x 22)

Q.4: The area of a circular ring formed by two concentric circles whose radii are 5.7 cm and 4.3 cm, respectively.

Solution: Let the radii of inner and outer circles be r 1 and r 2 , respectively.

Area of circular ring = area of outer circle – area of inner circle

= π r 2 2 – π r 1 2

= π (r 2 2 – π r 1 2 )

= π (r 2 – r 1 ) (r 2 + r 1 )

= =π(5.7−4.3)(5.7+4.3)

= π×1.4×10 sq. cm

=3.1416×14sq.cm.

=43.98 sq. cm

Q.5: What is the area of the circle that can be inscribed in a square of side 6 cm?

Square of side = 6 cm

Diameter of circle inscribed in the square = side of square = 6cm

Radius = 6/2 = 3 cm

Area of the circle inscribed = πr 2

Q.6: The circumference of a circle increases from 4π to 8π. Find the ratio of areas.

Solution: Let us say,

Circumference of first circle, C 1 = 4π

Circumference of new circle, C 2 = 8π

Area of old circle, A 1 = πr 1 2

Area of new circle, A 2 = πr 2 2

A 1 /A 2 = (πr 1 2 /πr 2 2 )

= (r 1 /r 2 ) 2

Therefore, the ratio of the areas of circles is 1:4.

Q.7: What is the area of the sector of a circle of radius 6 cm whose central angle is 30°?

Radius of circle = 6 cm

Central angle, θ=30°

Area of sector = θ/360 (πr 2 )

= 30/360 (π6 2 )

= 9.42 cm 2

Q.8: The radius of a circle is 17.5 cm. What is the area of the sector of the circle enclosed by two radii and an arc 44 cm in length?

Radius of a circle = 17.5 cm

Length of arc of circle = 44 cm

Area of sector = ½ × Arc Length × Radius

= ½ × 44 × 17.5

Q.9: A park is of the shape of a circle of diameter 7 m. It is surrounded by a path with a width of 0.7 m. If its cost is Rs.110 per sq. m., what is the expenditure of cementing the path?

Diameter of park = 7 m

Radius of park, r = 7/2 = 3.5 m

Width of park = 0.7 m

Radius of park along with path, R = 3.5 + 0.7 = 4.2 m

Cost per square meter = Rs.110

Area of path = Area of outer circle – area of inner circle

= πR 2 – πr 2

= π(R 2 – r 2 )

= 22/7 (4.2 2 – 3.5 2 )

= 22/7 (17.64 – 12.25)

= 16.94 m 2

Cost of expenditure of cementing the path = Rs. 110x 16.94 = Rs.1863.40

Q.10: The circumference of a given circular park is 55 m. It is surrounded by a path of uniform width 3.5 m. Find the area of the path.

Solution: Let r be the radius of the circular park.

r = 55/2π = 8.75 m

Area of park = π × (8.75) 2 = 240.625 m 2

Radius of the circular park with path, R = 8.75 + 3.5 = 12.25 m

Area of circular region is A = π × (12.25) 2 = 471.625 m 2

Area of the path surrounding the circular park = 471.625−240.625=231m 2

Video Lessons on Circles

Introduction to circles.

Parts of a Circle

• Area of a Circle

All about Circles

Related Articles

• Segment and Area of a Segment Of Circle
• Area Of Shapes
• Area Of Sector Of A Circle
• Circumference of a Circle

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Case Based Questions Test: Areas Related to Circles - 1 - Class 10 MCQ

10 questions mcq test - case based questions test: areas related to circles - 1, read the following text and answer the following question on the basis of the same: a horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure). what is the area of the grass field.

Read the following text and answer the following question on the basis of the same: A horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure). The grazing area if the rope were 10 m long instead of 5 m.

• A. 7.85 m 2
• D. 78.5 m 2

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Read the following text and answer the following question on the basis of the same: A horse is tied to a peg at one corner of a square shaped grass field of sides 15 m by means of a 5 m long rope (see the given figure). The given problem is based on which concept?

• A. Coordinate geometry
• B. Area related to circles
• D. None of these

The bigger part is known as major segment and smaller one is called minor segment.

Area of major segment OAQB = πr 2 - area of minor segment APB.

Area of segment of a circle = Area of the corresponding sector - Area of the corresponding triangle.

Read the following text and answer the following question on the basis of the same:

In a workshop, 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 as shown in the given figure.

What is the circumference of the brooch?

What is the area of the each sector of the brooch?

∴ Area of each sector

Areas Related to Circles

Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend, who is a partner in the competition, suggests two designs given below.

Observe these carefully.

Design I: This design is made with a circle of radius 32 cm leaving equilateral triangle ABC in the middle as shown in the given figure.

Design II: This Pookalam is made with 9 circular design each of radius 7 cm.

Refer Design I: The side of equilateral triangle is

Join OA, OB and OC

OA = OB = OC = Radius of circle = 32 sm

Let’s consider △OBC

Let’s draw OM ⊥ BC

By symmetry,

In right triangle △OMB

BC = 2 x BM

Areas Related to Circles Pookalam is the flower bed or flower pattern designed during Onam in Kerala. It is similar as Rangoli in North India and Kolam in Tamil Nadu. During the festival of Onam, your school is planning to conduct a Pookalam competition. Your friend, who is a partner in the competition, suggests two designs given below.

Refer Design II: The area of square is

• A. 1264 cm 2
• B. 1764 cm 2
• C. 1830 cm 2
• D. 1944 cm 2

diameter = 2 × 7 cm

side of square = 14 cm + 14 cm + 14 cm

Area of square = side 2

= (42 cm) 2

= 1764 cm 2

• A. 378 cm 2
• B. 260 cm 2
• C. 340 cm 2
• D. 278 cm 2

= 1386 cm 2

Area of square = 1764 cm 2

Area of remaining portion of square ABCD

= Area of square – Area of 9

circular design

= 1764 cm 2 – 1386 cm 2

A brooch is a small piece of jewellery which has a pin at the back so it can be fastened on a dress, blouse or coat. Designs of some brooch are shown below. Observe them carefully.

Design A: Brooch A is made with silver wire in the form of a circle with diameter 28 mm. The wire used for making 4 diameters which divide the circle into 8 equal parts.

Design B: Brooch b is made two colours i.e. Gold and silver. Outer part is made with Gold. The circumference of silver part is 44 mm and the gold part is 3 mm wide everywhere.

= 1/8 x Area of Brooch

Refer to Design B The difference of areas of golden and silver parts is

= Area of silver - Area of golden

= Area of circle of radius 10mm - Area of circle of radius 7mm

= π(10) 2 - π(7) 2

= 100π - 49π

--> and get INR 200 additional OFF

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Important Questions for Case Based Questions Test: Areas Related to Circles - 1

Case based questions test: areas related to circles - 1 mcqs with answers, online tests for case based questions test: areas related to circles - 1.

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