Mathematics is a subject requiring high knowledge and skills. For one to be good at Mathematics, one must be thorough with the vital concepts and also be comfortable with calculations. Hence, students should know all the techniques associated with the study of Mathematics.
Class 9 Mathematics Chapter 13 is more of a kind of chapter of mensuration covered in lower classes. In order to score well in this chapter, one must be through with all the formulas mentioned in the chapter. The main topics covered in NCERT Class 9 Mathematics Chapter 13 include the total and lateral surface area of cube, cuboid, cylinder, cone and sphere. You will also be acquainted with how to find the volume of cubes, cuboids, cylinders, cones and spheres.
The chapter has been covered in detail in NCERT Solutions for Class 9 Mathematics Chapter 13. Students can find all the formulas compiled in quick notes format, which will facilitate them to quickly grasp the topics in this chapter. Students will also be able to apply these formulas as required in the problems once they refer to our NCERT Solutions.
All the students taking the guidance from Extramarks and following Extramarks resources have seen a lot of changes in their results and have turned out to be great academic performers. Thus, becoming confident and developing a strong personality. You can find all the study material required for your preparation on the Extramarks website.
Key Topics Covered In NCERT Solutions for Class 9 Maths Chapter 13
Mensuration has always been an important part of Geometry as it covers the detailed study of the calculation of areas of 2D and 3D shapes. The chapter surface areas and volumes are another name for mensuration. As the name suggests, the chapter covers all the formulas associated with cube, cuboid, cylinder, cone and sphere in calculating their surface areas and volumes. Thus, it is more of a formula learning-oriented chapter for the students.
Students should read and revise the formulas as much as they can in order to be thorough with the chapter. NCERT Solutions Class 9 Mathematics Chapter 13 has covered all the major points related to this chapter in a very precise manner aiding students to get rid of the fear of multiple formulas included in this chapter. Students can get NCERT Solutions for Class 9 Mathematics Chapter 13 from the Extramarks’ website.
NCERT Solutions for Class 9 Mathematics Chapter 13 requires students to use solutions, reasoning, thinking skills, and facilities in solving sums with a better approach.
Introduction
In this chapter, we will learn about shapes like cuboids, cubes, circular cylinders, circular cones, spheres, etc., and we will learn to find out their surface area and their volume.
Surface area of cuboid and cube
In this part of the chapter, we will find out the surface area of the cuboid and cube. You can use the following formula for the surface area of the cuboid and the cube:
- Surface area of cuboid = 2(lb + bh + hl)
- Surface area of cube = 6a2.
You can find multiple examples to practise and learn more about this section in our NCERT Solutions for Class 9 Mathematics Chapter 13, available on the Extramarks’ website.
Surface area of a right circular cylinder
In this part of the chapter, we will find out the surface area of the right circular cylinder using the formula:
- Total surface area of right circular cylinder = 2πr(r + h)
Surface area of a right circular cone
In this part of the chapter, we will find out the surface area of the right circular cone. The total surface area of the right circular cone is given by:
- Total Surface area of the right circular cone = πr(l + r)
Surface area of a sphere and hemisphere.
In this part of the chapter, we will find out the surface area of the sphere and hemisphere. The formulas are as follows:
- Surface area of sphere = 4πr2
- Surface area of hemisphere = 2πr2.
For more details regarding the chapter and to find solutions to all the exercises given in the chapter in the NCERT Solutions for Class 9 Mathematics Chapter 13.
Volume of cuboid and cube
In this part of the chapter, we will find out the volume of the cuboid and cube. Their volume can be calculated by using the formula:
- Volume of cuboid = lbh
- Volume of cube = a3
Volume of cylinder
In this part of the chapter, we will find out the volume of the cylinder. The formula for the calculation of volume is
- Volume of cylinder = πr2h
Volume of a right circular cone.
In this part of the chapter, we will find out the Volume of a right cylinder cone using the formula:
- Volume of a right cylinder cone =⅓* πr2h
Volume of a sphere
In this part of the chapter, we will find out the volume of a sphere and volume of a hemisphere using the formula listed below:
- Volume of a sphere = 4/3*πr3
- Volume of a hemisphere = 2/3*πr3
Summary
In this chapter, we covered all about the 2D and 3D shapes and the formulas to calculate their areas
Surface area
- Surface area of cuboid = 2(lb + bh + hl)
- Surface area of cube = 6a2
- Total Surface area of right circular cylinder = 2πr(r + h)
- Total Surface area of right circular cone = πr(l + r)
- Surface area of sphere = 4πr2
- Surface area of hemisphere = 2πr2
Volume
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- Volume of cuboid = lbh
- Volume of cube = a3
- Volume of cylinder = πr2h
- Volume of a right cylinder cone =⅓* πr2h
- Volume of a sphere = 4/3*πr3
- Volume of a hemisphere = 2/3*πr3
The chapter is completely covered in detail in the NCERT Solutions for Class 9 Mathematics Chapter 13 available on the Extramarks’ website.
NCERT Solutions for Class 9 Maths Chapter 13: Exercise & Solutions
Even if one is thorough with all the formulas included in the chapter surface areas and volumes, one must be able to solve the problems accurately till the last step and be able to get the right answers. This mastery comes with a lot of practice. For this reason, we have included solutions to all the exercises given in the NCERT textbook in our NCERT Solutions for Class 9 Mathematics Chapter 13 in a detailed manner. One can also find extra questions related to the chapter on our Extramarks’ website, a trusted source for all the NCERT-related study material.
You can find for exercise specific questions and solutions for NCERT Solutions for Class 9 Mathematics Chapter 13 by referring to the following links:
- Chapter 13: Exercise 13.1 Question and answers
- Chapter 13: Exercise 13.2 Question and answers
- Chapter 13: Exercise 13.3 Question and answers
- Chapter 13: Exercise 13.4 Question and answers
- Chapter 13: Exercise 13.5 Question and answers
- Chapter 13: Exercise 13.6 Question and answers
- Chapter 13: Exercise 13.7 Question and answers
- Chapter 13: Exercise 13.8Question and answers
- Chapter 13: Exercise 13.9Question and answers
Along with NCERT Solutions for Class 9 Mathematics Chapter 13, students can explore NCERT Solutions on our Extramarks website for all primary and secondary classes.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT solutions Class 10
- NCERT solutions Class 11
- NCERT solutions Class 12
NCERT Exemplar for Class 9 Maths
Students must include NCERT Exemplar Class 9 Mathematics in their core study material as the book is designed by the subject matter experts. Thus, it helps students to get an idea of the types of questions they would have to face in their examinations. As a result, students find their examination papers easy after solving questions from the NCERT Exemplar.
The book is designed as per the latest CBSE syllabus. Students can promise themselves success in every examination they face after practising from this book. It has proved to be fruitful for the teachers too in framing their question papers, thus becoming an important resource for the students as well as teachers.
Learning to solve the problems in a well stipulated time is quite necessary to complete the entire examination in a given time frame. Hence, NCERT Exemplar provides quick tips and tricks to solve every sum, thereby making calculations easy. You can get NCERT Exemplar Class 9 Mathematics from the Extramarks’ website today.
Key Features of NCERT Solutions for Class 9 Maths Chapter 13
Students with good calculating skills always excel in Mathematics. Hence, in NCERT Solutions for Class 9 Mathematics Chapter 13, we have covered various aspects which help in making the calculations of the students strong. The key features are as follows:
- Multiple Questions are covered from all the topics and sub-topics of the chapter in the NCERT Solutions for Class 9 Mathematics Chapter 13, keeping in mind no concept remains untouched
- All sets of questions right from basic to advanced, are covered noting the levels of different kinds of students
- All the questions are covered as per the latest CBSE curriculum.
- After completing the NCERT Solutions for Class 9 Mathematics Chapter 13, students will be able to distinguish between the areas and volumes of different figures easily and confidently.