NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas Volumes are the best guide for you. These solutions will help you understand how to solve the questions of Surface Areas and Volumes in the board exams and score full marks. You can download the exercise-wise NCERT Solutions for Class 10 Maths Chapter 13 Surface Areas and Volumes and practice the exercises at your own pace. These solutions are prepared by askIITians Maths experts as a free study guide for every student. Download them in PDF form today and start practising!
In the earlier classes, you have studied how to find the surface area and volume of cubes, cuboids and cylinders. Now, in Class 10 Maths Chapter 13, you will study how to find the surface areas and volumes of combinations of solids. This chapter also includes finding areas and volumes while converting one solid shape into another (surface area and volume of combinations of solids). There are a lot of important formulae and calculations in this chapter that you must take care of. You must match all your answers with our NCERT Class 10 Maths Solutions.
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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 |
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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 |
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Sphere |
4πr2, where r is the radius of the sphere |
Not applicable |
(4/3)πr3 |
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Hemisphere |
2πr2, where r is the radius of the hemisphere |
πr2, where r is the radius of the hemisphere |
2/3πr3 |
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Frustum of a Cone |
πl (r 1 + r2 ) + πr12 + πr22 |
π (r 1 + r2 )l |
1/3 πh (r12 + r22 + r 1r2) |
NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.1
The first exercise of this chapter is based on finding the surface area of a combination of solids. For instance, a combination of a hemisphere and a cylinder, a combination of a cone and a hemisphere, a combination of a cube and a hemisphere, a combination of a cone and a cylinder and more. There are 9 questions in this exercise of word-problems format. You must read the word problems very carefully and make sure to use the right formula for curved surface area and total surface area. Our NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.1 will help you out.
NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.2
The second exercise of this chapter is based on finding the volume of a combination of solids. There are 8 questions in this exercise and all of them are word problems. You must read them carefully and take note of all the data that is given to you. In some questions, the volume of a combination of solids would increase after the combination while in some questions it would increase. We have provided stepwise solutions for the exercise. Check them if you get stuck at any point in solving this exercise.
NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.3
The third exercise of the chapter is based on finding the surface area and volume on converting one solid to another. For instance, a cuboid might be melted and converted into several cubes, or a cone may be converted into a sphere. You have to read the questions carefully and determine whether you have to find the volume or surface area. The exercise includes 9 interesting word problems. Make sure you match your answers with our NCERT Solutions.
NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.4
The fourth exercise of the chapter is based on finding the curved surface area, total surface area and volume of the frustum of a cone. The frustum of the cone is obtained when we slice (or cut) through a cone with a plane parallel to its base and remove the cone that is formed on one side of that plane. For instance, a bucket is in the shape of a frustum of a cone. The exercise includes 5-word problems. This is a new concept so practice all the questions very carefully.
NCERT Solutions for Class 10 Maths Chapter 13 Ex 13.5
The last exercise of the chapter is optional which means that the questions given in this exercise will not be asked in the final examination of Class 10. The exercise includes 7 miscellaneous questions based on all the concepts given in this chapter. The questions in this exercise are of advanced level so you might need some assistance in solving them. You can download our NCERT Solutions for Class 10 Maths Chapter 13 and solve all your queries in no time.
Key features of NCERT Class 10 Maths Solutions for Chapter 13 Surface Areas and Volumes:
There are 5 exercises and 38 questions in NCERT Class 10 Maths Chapter 13 Surface Areas and Volumes. askIITians experts have solved each exercise of the chapter for your reference.
askIITians provides flashcards and revision notes to help you memorise all the important formulae of the chapter. You must practice all the NCERT exercises and solved examples for your complete understanding of the chapter. In case of any confusion, just refer to our NCERT Solutions and resolve your queries.
askIITians provides a plethora of study resources like revision notes, practice papers, mind maps, flashcards, previous year papers, important questions, extra questions, NCERT Solutions and more to help you practice each chapter of Class 10 Maths thoroughly. You can also take our online live classes and study directly from our Maths experts in live, interactive classes.