Are you looking for NCERT Solutions for Class 9 Maths Chapter 13? End your search here as the askIITians team has prepared step by step solutions for all the exercise questions of the Surface Areas and Volumes chapter. These solutions will help you understand all the concepts introduced in this chapter and you will be able to prepare well for your exams. All these solutions are available for free to all students. They are based on the latest syllabus for the academic year 2022.
In junior classes, you must have studied finding the area of shapes like rectangle, circle, triangle, rhombus, parallelogram, etc. You would have also studied volume or capacity. This chapter introduces you to find the area and volume of three-dimensional objects like the right circular cylinder, cuboid, cube, etc. Before you start solving the NCERT exercises of this chapter, you must take note of the following:
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Important formulae for NCERT Class 9 Maths Chapter 13 |
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3D Shape |
Total Surface Area (TSA) |
Curved Surface Area (CSA) |
Volume |
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Cube |
6a2 |
4a2, where a is the length of each side |
a3 |
|
Cuboid |
2 (lb + bh + lh) |
2h (l + b), where l, b, and h are the length, breadth, and height of the cuboid |
l × b × h |
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Cone |
πr(r + l) |
πrl, where r is the radius and l is the slant height of the cone |
(1/3)πr2h |
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Cylinder |
2πr(h + r) |
2πrh, where r is the radius and h is the height of the cylinder |
πr2h |
|
Sphere |
4πr2, where r is the radius of the sphere |
Not applicable |
(4/3)πr3 |
Chapter 13 Surface Areas and Volumes includes 9 exercises each of which is very important from the exam perspective. This chapter is quite scoring as you only need to learn how to apply the surface area or volume formula and calculate the answer. So, just memorise the formulae and strengthen your calculations. Let us see what each exercise of this chapter includes and how many questions you have to solve in each exercise.
The first exercise of the Surface Areas and Volumes chapter includes 8 questions. This exercise is based on finding the surface area of a cube and cuboid. However, the questions in the exercise are not straightforward. For instance, in exercise question number 2 you not only have to find the surface area of a room whose length, breadth and height are given to you but you also have to find the cost of washing the walls and the ceiling.
You can easily solve this exercise if you read the questions carefully and take note of all the data given in the questions.
The second exercise of the Surface Areas and Volumes chapter is based on finding the surface area of a right circular cylinder. There are 11 questions in this exercise and all of them are very interesting to solve. For instance, in question 7 you are given the inner diameter of a well and its depth. You have to find the cost of plastering the inner curved surface area.
The third exercise of this chapter is based on finding the surface area of a right circular cone. There are 8 questions in this exercise and all of them are easy to solve. However, you must take care of the calculations as a single error can lead you to a wrong answer. For example, in question 5 you have to find the total material required to build a tent in the shape of a cone. You are also given the length of extra cloth required.
The fourth exercise of this chapter is based on finding the surface area of a sphere and a hemisphere. The sphere is already curved so it has one surface area only. However, a hemisphere may have curved surface area and total surface area respectively. There are just 9 questions in this exercise. It also includes the applications of topics learned in previous exercises such as the surface area of a right circular cylinder. Our NCERT solutions include step by step details of how to solve this exercise without making any calculation mistakes.
The fifth exercise of the Surface Area and Volume chapter includes concepts like the volume of a cuboid and the volume of a cube. The formula for finding the volume of a cube or a cuboid is very easy and you can memorise it in minutes. However, this exercise includes a special category of questions where you have to find how many cubes can be made out of a cuboid. Such as in question 7 where you have to find out how many wooden crates can be stored in a room. Both of them have the shape of a cuboid. So you have to find how many smaller cuboids can fit in a bigger cuboid. In case you have any doubts about solving such questions in this exercise, you must check our free NCERT solutions for Class 9 Maths Chapter 13.
The sixth exercise is based on finding the volume of a cylinder. The exercise includes 8 questions based on the application of the formula for the volume of a cylinder. It includes questions like finding the radius of the base of the right circular cylinder and its volume if its surface area is given to you. This means you must have studied the topics given in the previous sections to master this exercise.
The seventh exercise of Class 9 Maths Chapter 13 is based on finding the volume of a right circular cone. There are 9 questions in this exercise and not all of them are straightforward. This is why many students get confused in solving this exercise. For example, in question 6, you are given the volume and the diameter of the cone and you have to find the height of the cone, slant height of the cone and the curved surface area of the cone. Our NCERT solutions are the perfect guide to understand how to solve complex questions easily.
The eighth exercise of the Surface Area and Volume chapter is based on finding the volume of a sphere and a hemisphere. There are 10 questions in this exercise all based on the application of the formulas for finding the volumes of a sphere and a hemisphere. You must solve every question carefully as the chances of making calculation mistakes is more in this exercise. If you get stuck, our pre-written NCERT online solutions will come in handy. Just download them and refer to them to solve your query.
The last exercise of this chapter is optional. But our faculty highly recommends every student to solve this exercise as well because it will help them in brushing up all the formulae that they have learned in this chapter. There are just three questions in this exercise but all of them are complex. For example, the last question asks students to find out by what per cent does the curved surface area of a sphere would decrease if its diameter is decreased by 25%.
NCERT solutions are not made to make you cheat the answers but to help you how to solve the questions that you find difficult. Not every student gets a chance to ask queries in a timed class but if you have these solutions, you can solve your queries at any time. askIITians online Maths NCERT solutions are important for every Class 9 student because:
Every chapter of the Class 9 NCERT textbook is important. Chapter 13 especially is a simple chapter if you memorise all the formulae correctly. It includes some application-based questions but you can easily master them with practice. Moreover, this chapter is also important from the Class 10 board exams since you will study surface area and volume in Class 10 as well.
To use askIITians NCERT solutions effectively, Class 9 students must practice all the questions on their own first. If they get stuck at any place or are unable to find the right answer, they must check the online NCERT solutions and resolve their queries.
Class 9 Maths solutions act as a self-explanatory guide for the students that they can refer to at any time. These solutions help in solidifying the concepts taught in the Class 9 NCERT textbook and hence help them prepare well for their exams.
Chapter 13 Surface Area and Volume of Class 9 Maths NCERT textbook include 9 exercises and 75 questions in total. All these questions help students in solidifying their concepts about surface area and volume of different three-dimensional shapes like cube, cuboid, sphere, hemisphere, right circular cylinder, etc.
Yes, askIITians faculty recommends that every exercise given in the NCERT textbook is important for the students as it helps them understand the concepts better. The more you practice, the easier it will be to solve questions in the exam.