NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles (Ex 12.1)
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Class 10 is a pivotal academic year in students’ lives. They take the board exams for the very first time in Class 10. As a result, students must study hard for their Class 10 exams. Class 10 board exams are extremely important; the marks secured in the board exams often play a significant role in determining which subject stream students will pursue in Class 11. The Central Board of Secondary Education (CBSE) holds annual Class 10 board examinations in pen and paper format. Students in the CBSE Board Examinations for Class 10are advised to read NCERT books. Every year, the National Council of Educational Research and Training publishes the NCERT books. NCERT books are extremely beneficial to learners in their preparation. The NCERT textbooks are written in simple language that most students can understand. NCERT textbooks also include diagrams, facts, and figures to aid visual learning. The exercises given at the end of each chapter are essential and must be completed by all students.
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ToggleSignificance of Class 10: Many times, admission to higher secondary schools of students’ choice is based on the results of the Class 10 board exams. Board exam results are an important part of a student’s academic history because they show their academic performance and accomplishments. Many prestigious colleges and universities consider Class 10 marks when admitting students. As a result, a strong performance in the Class 10 board exams can help a student’s career. Furthermore, a student must have obtained a minimum required percentage/grades in the Class 10 board exams in order to enrol in any entrance exam or scholarship programme available after Class 10.
Mathematics is a very crucial foundational subject. It is the foundation for all other subjects. A variety of Physics, Chemistry, and Biology ideas and principles are explained using Mathematical concepts. It is also applied to Social Science research in the form of statistics. Economics and Business both use statistics. In addition, practically all competitive exams assess logical acumen and thinking. Mathematics up to class 10 is also typically covered in competitive exam syllabi.
Knowledge of Mathematics can be important for pursuing jobs in a range of fields. Students can use its principles to pursue careers in Computer Science, Engineering, Astronomy, Statistics, Data Science, and other fields. Students interested in these occupations should emphasise Class 10 Mathematics. Class 10 Mathematics is critical for students to understand the fundamental principles of all subjects. Therefore, students should study effectively for Class 10 Mathematics.
Mathematics is a core subject in Class 10. All the chapters of Class 10 Mathematics are important for students and must be prepared effectively. To prepare for the Class 10 Chapter 12 Maths Exercise 12.1 students can refer to the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 are available to download from the Extramarks’ website and mobile application. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 will guide students to solve all the questions from Exercise 12.1 Maths Class 10. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 can be downloaded in PDF format for easy access.
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles (Ex 12.1) Exercise 12.1
Chapter 12 of Class 10 Mathematics is named Areas Related To Circles. Chapter 12 comes under the unit on Mensuration. The unit on Mensuration holds a total of 10 marks weightage in the CBSE board examinations. Therefore, students must prepare for this entire unit in detail. In Chapter 12, students learn about various concepts related to a Circle. Students learn about the Perimeter, Area of a Circle, Area of Sector, and Segment of a Circle etc. All the mentioned topics are very important to score well in the board examinations. Students must solve all the exercise questions in this chapter. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 can be downloaded from the website and mobile application of Extramarks.The NCERT Solutions for Class 10 Maths, Chapter 12, Exercise 12.1 can be downloaded from Extramarks’ website and mobile app.
From the link given below, students can download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 will help students solve all the questions from Class 10 Maths Ex 12.1.
NCERT Solutions for all classes and all subjects are available on the Extramarks website and mobile application. The NCERT Solutions Class 12, NCERT Solutions Class 11, NCERT Solutions Class 10, NCERT Solutions Class 9, NCERT Solutions Class 8, NCERT Solutions Class 7, NCERT Solutions Class 6, NCERT Solutions Class 5, NCERT Solutions Class 4, NCERT Solutions Class 3, NCERT Solutions Class 2, NCERT Solutions Class 1 for all subjects can be downloaded from the Extramarks website and mobile application. The resources provided by Extramarks are the best study materials for students to score well in their board examinations. All the resources provided by Extramarks are updated regularly according to the latest CBSE guidelines. Therefore, students can use these resources without any worry. Moreover, Extramarks’ study materials cover the entire syllabus holistically without missing out on any important topic. With the help of Extramarks’ study resources, students will be able to fetch good marks in all Class 10 subjects.
Extramarks also provides study materials for Hindi medium students. Moreover, Extramarks provides study resources for students from ICSEaffiliated schools. The ICSE curriculum is covered holistically in the resources offered by Extramarks. To get good grades, students must use the Extramarksresources.Access NCERT Solutions for Class 10 Mathematics Chapter 12 – Areas Related To Circles
Students can access the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 from the link provided. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 will help students strengthen their core concepts from this chapter.Students must download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 in PDF format from the website and mobile application of Extramarks.
NCERT Solutions for Class 10 Maths Chapter 12 Areas Related To Circles Exercise 12.1
Importance of NCERT exercises: For any subject, NCERT books are recommended by experts to prepare for board examinations. NCERT exercises help students to check their knowledge of the subject. They guide the students to prepare for their examinations. Students must solve all the questions from Class 10 Maths Chapter 12 Exercise 12.1 to prepare effectively for Chapter 12. Moreover, NCERT solutions are very important as they give students an idea of what kind of questions are going to be asked in the exam. In some cases, NCERT exercises directly contribute to questions. To find the most authentic solutions for Chapter 12 Exercise 12.1, students must refer to the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 are available to download from the Extramarks website and mobile application. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 are the best resources for students to solve questions of Chapter 12.
Apart from the NCERT exercises, students must also solve the CBSE sample question papers and past years’ papers. Students must complete these sample papers because they are crucial for providing insight into the types of questions that will appear. Additionally, the sample papers made available by Extramarks are created in accordance with the most recent CBSE regulations. Past years’ papers also help students in identifying the trends in the question papers. With the help of these papers, students will be able to selfassess their preparation level. Students must identify their weak points and regularly practise questions on them.With ample practice, students will be able to solve most of the questions that will be asked in the board examination. If students face any challenges in solving the past years’ papers and sample papers, they can refer to the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1. They can also use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 to prepare short notes of all the important formulas and questions from this chapter. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 can be downloaded in PDF format from the website and mobile application of Extramarks.
NCERT Solutions for Class 10 Maths
From the Extramarks platform, students can download NCERT solutions for all chapters of Class 10 Math. By referring to the NCERT solutions offered by Extramarks, students can get access to the most precise solutions. All solutions offered by Extramarks are written in a stepwise manner for the benefit of students. Students can download the NCERT exercise solutions in PDF format.
Access Other Exercise Solutions of Class 10 Maths Chapter 12 Areas Related to Circles
Extramarks also provides NCERT solutions for all Class 10 Maths Chapter 12 exercisesStudents can find the NCERT solutions for Exercise 12.2 Chapter 12 and Exercise 12.3 Chapter 12 Class 10 from the website and mobile application of Extramarks. With the help of these NCERT solutions, students will be able to prepare for the entire chapter.. Students are advised to begin by answering simple questions for practise before moving on to Higher Order Thinking Skills (HOTS) questions.
Q.1 The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.
Ans
$\begin{array}{l}\text{It is given that the radii of first and second circles are}\\ \text{19 cm and 9 cm respectively.}\\ \text{Let the radius of the third circle is r.}\\ \text{According to question,}\\ \text{Circumference of the third circle}=\text{Sum of the circumferences}\\ \text{of the first and second circles}\\ \text{or 2}\mathrm{\pi}\text{r}=2\mathrm{\pi}\times 19+2\mathrm{\pi}\times 9=2\mathrm{\pi}(19+9)\\ \text{or 2}\mathrm{\pi}\text{r}=2\times 28\times \mathrm{\pi}\\ \text{or r}=\frac{2\times 28\times \mathrm{\pi}}{2\times \mathrm{\pi}}=28\text{cm}\\ \text{Therefore, the radius of the circle which has circumference}\\ \text{equal to the sum of the circumferences of the given circles}\\ \text{is 28 cm.}\end{array}$
Q.2 The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Ans
$\begin{array}{l}\text{It is given that the radii of first and second circles are}\\ \text{8 cm and 6 cm respectively.}\\ \text{Let the radius of the third circle is r.}\\ \text{According to question,}\\ \text{Area of the third circle}=\text{Sum of the areas of the}\\ \text{first and second circles}\\ \text{or}\mathrm{\pi}{\text{r}}^{2}=\mathrm{\pi}\times {8}^{2}+\mathrm{\pi}\times {6}^{2}=\mathrm{\pi}(64+36)\\ \text{or}\mathrm{\pi}{\text{r}}^{2}=100\mathrm{\pi}\\ \text{or r}=\sqrt{100}=10\text{cm}\\ \text{Therefore, the radius of the circle which has area}\\ \text{equal to the sum of the areas of the given circles}\\ \text{is 10 cm.}\end{array}$
Q.3 The following figure depicts an archery target marked with its five scoring areas from the centre outwards as Gold, Red, Blue, Black and White. The diameter of the region representing Gold score is 21 cm and each of the other bands is 10.5 cm wide. Find the area of each of the five scoring regions.
Ans
$\begin{array}{l}\text{Radius of the region representing Gold score}=\mathrm{r}=\frac{21}{2}=10.5\text{cm}\\ \text{It is given that each band}\left(\text{except gold}\right)\text{is 10.5 cm wide.}\\ \text{Therefore,}\\ \text{Radius of the outer circle of the Red score}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={\mathrm{r}}_{1}=10.5+10.5=21\text{cm\hspace{0.17em}}\\ \text{Radius of the outer circle of the Blue score}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={\mathrm{r}}_{2}=21+10.5=31.5\text{cm}\\ \text{Radius of the outer circle of the Black score}\\ \text{}={\mathrm{r}}_{3}\\ \text{}=31.5+10.5\\ \text{}=42\text{cm}\\ \text{Radius of the outer circle of the White score}\\ \text{}={\mathrm{r}}_{4}\\ \text{}=42+10.5\\ \text{}=52.5\text{cm}\\ \text{Now,}\\ \text{Area of the Gold score}={\mathrm{\pi r}}^{2}\\ \text{}=\frac{22}{7}\times \frac{21}{2}\times \frac{21}{2}\\ \text{}=346.5{\text{cm}}^{2}\\ \text{Area of the Red score}={{\mathrm{\pi r}}_{1}}^{2}\text{Area of the Gold score}\\ \text{}=\frac{22}{7}\times {21}^{2}346.5\\ \text{}=1039.5{\text{cm}}^{2}\\ \text{Area of the Blue score}={{\mathrm{\pi r}}_{2}}^{2}{{\mathrm{\pi r}}_{1}}^{2}\\ \text{}=\frac{22}{7}\times \{{(31.5)}^{2}{21}^{2}\}\\ \text{}=1732.5{\text{cm}}^{2}\\ \text{Area of the Black score}={{\mathrm{\pi r}}_{3}}^{2}{{\mathrm{\pi r}}_{2}}^{2}\\ \text{}=\frac{22}{7}\times \{{\left(42\right)}^{2}{(31.5)}^{2}\}\\ \text{}=2425.5{\text{cm}}^{2}\\ \text{Area of the White score}={{\mathrm{\pi r}}_{4}}^{2}{{\mathrm{\pi r}}_{3}}^{2}\\ \text{}=\frac{22}{7}\times \{{(52.5)}^{2}{\left(42\right)}^{2}\}\\ \text{}=3118.5{\text{cm}}^{2}\end{array}$
Q.4 The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?
Ans
$\begin{array}{l}\text{It is given that the wheels of a car are of diameter 80 cm each.}\\ \text{Therefore, circumference of each wheel}=\mathrm{\pi d}=\frac{22}{7}\times 80\\ \\ \text{Speed of the car}=66\text{km/h}=\frac{66\times 1000\times 100}{60\text{}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=110000\text{cm/minute}\\ \text{Distance covered by the car in 10 minutes}=11,00,000\text{cm}\\ \text{Number of revolutions made by each wheel to}\\ \text{cover}11,00,000\text{cm}=\frac{11,00,000\text{}}{\frac{22}{7}\times 80}=4375\end{array}$
Q.5 Tick the correct answer in the following and justify your choice: If the perimeter and the area of a circle are numerically equal, then the radius of the circle is
(A) 2 units (B) π units (C) 4 units (D) 7 units
Ans
$\begin{array}{l}\text{Let the radius of the circle be}\mathrm{r}.\\ \text{Given that,}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}Circumference of the circle}=\text{Area of the circle}\\ \text{or\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}2\mathrm{\pi r}={\mathrm{\pi r}}^{2}\\ \text{or 2}=\mathrm{r}\\ \text{Therefore, radius of the circle is 2 units.}\end{array}$
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FAQs (Frequently Asked Questions)
1. From where can students and parents download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1?
Students and parents can find the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 on the Extramarks website and mobile application.
2. Can the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 be downloaded in PDF format?
Yes, students can download the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 in PDF format. The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 are available to download from the website and mobile application of Extramarks.
3. Can students use the Extramarks’ NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 to solve CBSE sample papers and past years’ papers before the examinations?
Yes, students can use the Extramarks’ NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 to solve CBSE sample papers and past years’ papers before the examinations as this helps them in understanding the marks distribution, syllabus and much more.
4. How will Extramarks’ NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 help students in the preparation for their board examinations?
Learners can use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 for making brief notes, and for revisiting essential formulas a few days before the exams. Students can also use the NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 for selfassessment of their preparation. This will help them to identify their weak areas and will enable them to work on them.
5. Does the Extramarks’ NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 contain NCERT solutions for all questions of Class 10 Mathematics Chapter 12?
The NCERT Solutions For Class 10 Maths Chapter 12 Exercise 12.1 contain the NCERT solutions for all the NCERT questions of Class 10 Mathematics Chapter 12 Exercise 12.1. It contains authentic solutions for all the questions from that exercise.
6. Where can students find the solutions for other NCERT Class 10 books?
Students can find the solutions for other NCERT Class 10 books on the Extramarks website and mobile application. Extramarks provides NCERT solutions for all classes from Class 1 to Class 12 in all subjects. Extramarks also provides resources such as revision notes, and past years’ paper solutions too for the benefit of students with their exam preparation.