Surface Areas and Volumes Class 10 Notes CBSE Maths Chapter 12 (Free PDF Download)

The concept of surface areas of different shapes and their volumes can be easily understood if you follow how the formulas are prepared. In this chapter, you will study how the surface area of different shapes such as cubes, cuboids, cylinders, cones and spheres can be calculated. In fact, this chapter will also introduce how the surface area of the curved shapes can be identified. 

The total surface area, curved surface area and lateral surface area of these 3-dimensional structures will be studied in this section. With the help of the revision notes of Class 10 Maths Chapter 12, you can easily understand how the formulas have been determined to calculate the area of these shapes by availing a few dimensions. To make sure that you grab the concepts of Class 10 mathematics properly, the experts of Vedantu have prepared revision notes for each chapter in the syllabus.

Let Us Take a Quick Look at the Surface Area and Volume of a Few Geometrical Shapes

A cuboid has three dimensions, its length, breadth and height. By using these dimensions, the surface area of the cuboid can be determined. As there are 6 surfaces, there are three pairs actually. Understanding how to calculate the lateral surface area of each of the three pairs will help you determine the formula. This formula is universal and can be used to calculate the lateral surface area of any cuboid. In fact, Class 10 Maths notes of Surface Areas and Volumes will also tell you how to specifically determine the area of a particular surface.

In the Ch 12 Class 10 Maths revision notes, if you proceed to a cube, you will find that all the dimensions are the same. It means that the length, breadth and height of a cube will be equal to each other.

If you proceed to the cylinder section, you will be familiarized with the concept of curved surfaces. Determining the area of the curved surface becomes easier when you have Class 10 revision notes Surface Areas and Volumes beside you. The formula of the curved surface of a right circular cone will also be described in such a way that you will find it quite easy to understand.

Why Should You Use Class 10 Revision Notes Maths Ch 12?

The experts of Vedantu have prepared Class 10 revision notes Maths Ch 12 in such a way that every common doubt that arises in the mind of students can be resolved perfectly.

Maths Class 10 Surface Areas and Volumes notes will help you properly describe how the formulas are formed and used to solve the exercise problems. The entire chapter will be properly described and clarified in such a way that students can figure out answering questions on their own.

The notes of Class 10 revision notes Chapter 12 will also help you revise the chapter within a short period. Find the specific sections in the revision notes to understand the specific 3-D shapes properly and enjoy studying the formula. Find the differences between the curved and lateral surface area and figure out how the formulas are formed to calculate them with the help of these revision notes.

Download Revision Notes Surface Areas and Volumes PDF

You can refer to the Class 10 Revision Notes Surface Areas and Volumes PDF for a quick revision of the types of sums covered in this chapter. Studying from these revision notes will help you prepare this chapter fast enough before the exams. Vedantu Notes of Class 10 Revision Notes Chapter 12 PDF play a very important role in self-study. Let us revise some important concepts and Formulas of Surface Areas and Volumes.

Surface Area

The surface area is the area occupied by a three-dimensional object. As the three-dimensional object is made up of 2D faces, the surface area is the sum of the areas of all the faces of the figure.

Basically, the Surface Area Can Be Classified As

• Curved Surface Area (CSA).

The curved surface area of an object is the area of all the curved surfaces in an object.

• Lateral Surface Area (LSA) 

The lateral surface is the area of all the faces of the object, excluding the area of its base and top.

• Total Surface Area (TSA) 

Total surface area is the area of all the faces including the bases.

Volume

The space occupied by the three-dimensional object is measured in terms of the volume of that object. The volume of a solid shape is the product of three dimensions, so the volume is expressed in cubic units. 

Important Formulas for Surface Areas and Volumes

Formulas for Lateral/ Curved Surface Area, Total Surface Area and Volume related to 3d Shapes(Solid shapes)

Surface Area and Volume of Cuboid

Lateral Surface Area of a Cuboid

The lateral surface area of the cuboid with length l, height h, and breadth b

= Area of AEHD + Area of BFGC + Area of ABFE + Area of DHGC

=2(b×h) + 2(l×h)

Total Surface Area of a Cuboid

Total surface area (TSA) of cuboid = Sum of the areas of all its six rectangular faces

=2 (l×b) + 2(b×h) + 2 (l×h)

Volume and Surface Area of Cube

Lateral Surface area of a cube

Lateral surface area (LSA) is the area of all the sides except the top and bottom faces.

Lateral surface area of cube = 2(a×a+a×a)=4a2

Total Surface Area of a cube

For cube, length = breadth = height = a

Total surface area (TSA) of the cube = 2 (a×a+a×a+a×a)

    = 2 × (3a2)

Surface Area and Volume of Right Circular Cone Right Circular Cylinder

The formula for the Lateral Surface Area or Curved Surface Area is given by 

Where,

r = radius of the circular base

h = height of the right circular cylinder 

= 3.14 or 22/7 

Total Surface Area of Right Circular Cylinder

Where,

r = radius of the circular base

h = height of the right circular cylinder 

𝜋 = 3.14 or 22/7 

Volume

The volume of Right Circular Cylinder(V)  = Area of the circular base x Height of the Right Cylinder

Surface Area and Volume of Right Circular Cone

Curved Surface Area

Total Surface Area

Volume 

Why Choose Vedantu?

1. Subject experts at Vedantu consult various reference books to prepare these notes.

2. Vedantu revision notes are very handy and can be used anytime from anywhere.

3. Class 10 Maths Notes of Surface Areas and Volumes PDF is available free of cost so that anyone can use it from anywhere anytime.

4. Revision Notes Class 10 Maths Chapter 12 PDF is also available offline. 

CBSE Vedantu Class 10 Maths Notes of Surface Areas and Volumes notes will provide you a summary of all the important and relevant topics from the Surface Areas and Volumes.

Important Formulas Related to Surface Areas and Volumes

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CBSE Vedantu Class 10 Maths Notes of Surface Areas and Volumes notes will provide you a summary of all the important and relevant topics from the Surface Areas and Volumes.

Other Maths Related Links

• Important Questions for Class 10

• CBSE Syllabus for Class 10

• CSBE Sample Papers for Class 10

• RS Aggarwal Solutions for Class 10

• Lakhmir Singh Class 10 Solutions

• NCERT Exemplar Class 10 Solutions

• NCERT Solutions for Class 10

• Revision Notes for Class 10

• NCERT Books for Class 10

• CSBE Previous Year Question Papers for Class 10

• Maths formulas for Class 10

• RD Sharma Class 10 Solutions
  
  

CBSE Class 10 Revision Notes - Other Chapters

The following is a list of links that take you to the revision notes that we have prepared for each chapter in the CBSE Class 10 syllabus. We recommend that students go through these links to reap the full benefits of our study materials. 

• Chapter 1 - Real Numbers Revision Notes

• Chapter 2 - Polynomials Revision Notes

• Chapter 3 - Pair of Linear Equations in Two Variables Revision Notes

• Chapter 4 - Quadratic Equations Revision Notes

• Chapter 5 - Arithmetic Progressions Revision Notes

• Chapter 6 - Triangles Revision Notes

• Chapter 7 - Coordinate Geometry Revision Notes

• Chapter 8 - Introduction to Trigonometry Revision Notes

• Chapter 9 - Some Applications of Trigonometry Revision Notes

• Chapter 10 - Circles Revision Notes

• Chapter 11 - Constructions Revision Notes

• Chapter 12 - Areas Related to Circles Revision Notes

• Chapter 14 - Statistics Revision Notes

• Chapter 15 - Probability Revision Notes
  

Conclusion

The chapter on Surface Areas and Volumes is included in the CBSE Class 10 Maths syllabus and is majorly formula based. Students who can learn, understand, and memorise these formulas can easily solve problems based on Surface Areas and Volumes. We have provided the revision notes for students to make use of during their exam preparation. We would advise students to go through these revision notes along with the other related links that we have provided in this article so that they don’t miss out on any important information.