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

Last updated date: 06th Sep 2024
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## Class 10 Maths Revision Notes for Surface Areas and Volumes of Chapter 12 - Free PDF Download

Class 10 Mathematics has a remarkable syllabus where students discover excellent chapters related to advanced concepts. These concepts will help you study the chapters in higher mathematics that you will study later. In this section, you will find Class 10 Maths Chapter 12 revision notes prepared by the experts to aid students in grabbing the concepts of surface areas and volumes of different shapes. You will find a proper description of the subject matter using simpler language so that you can easily relate to them while answering the questions. These revision notes are ideal to study when you have an exam coming. Use these notes by Vedantu as a reference and prepare the chapter properly.

Table of Content
1. Class 10 Maths Revision Notes for Surface Areas and Volumes of Chapter 12 - Free PDF Download
3. Surface Areas and Volumes: Revision notes Class 10 Maths Chapter 12
3.1Let Us Take a Quick Look at the Surface Area and Volume of a Few Geometrical Shapes
3.2Why Should You Use Class 10 Revision Notes Maths Ch 12?
3.4Surface Area
3.5Basically, the Surface Area Can Be Classified As
3.6Volume
3.7Important Formulas for Surface Areas and Volumes
3.8Surface Area and Volume of Cuboid
3.9Lateral Surface Area of a Cuboid
3.10Total Surface Area of a Cuboid
3.11Volume and Surface Area of Cube
3.12Lateral Surface area of a cube
3.13Total Surface Area of a cube
3.14Surface Area and Volume of Right Circular Cone Right Circular Cylinder
3.15Total Surface Area of Right Circular Cylinder
3.16Volume
3.17Surface Area and Volume of Right Circular Cone
3.18Curved Surface Area
3.19Total Surface Area
3.20Volume
3.21Why Choose Vedantu?
3.22Important Formulas Related to Surface Areas and Volumes
4. Why Choose Vedantu?
4.2CBSE Class 10 Revision Notes - Other Chapters
5. Conclusion
FAQs

Vedantu is a platform that provides free NCERT Solution and other study materials for students. You can download NCERT Solutions Class 10 Science to help you to revise the complete Syllabus and score more marks in your examinations.

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## Surface Areas and Volumes: Revision notes Class 10 Maths Chapter 12

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.

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)

### 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)

 LSA (cuboid) = 2h(l + b)

### 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)

 TSA (cuboid)= 2(lb + bh +lh)

### 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

 Lateral surface area of cube = 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)

 TSA(cube) = 6a2

### 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

 Lateral or Curved Area = 2 𝜋rh sq.units

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

 TSA = 2 𝜋 r (h + r) sq.units

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

 Volume(V) = πr2h

### Curved Surface Area

 Curved Surface Area of Cone=½ ( circumference of base ) x (slant height) = 𝜋r l

### Total Surface Area

 Total Surface Area of Right Circular Cone = 𝜋r( l + r)

### Volume

 Volume of Right Circular Cone = ⅓ 𝜋r2h

### 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

 Figure Perimeter Formula Total Surface Area Formula Curved Surface Area/Lateral Surface Area Formula Volume Formula Square 4 x side side x side - - Rectangle 2(w+h) w.h - - Parallelogram 2(a+b) b.h - - Trapezoid a+b+c+d 1/2{(a+b).h} - - Circle 2 π r π r2 - - Ellipse $2\Pi \sqrt{\frac{a^{2} + b^{2}}{2}}$ π a.b - - Triangle a+b+c 1/2 ( b * h) - - Cuboid 4(l+b+h) 2(lb+bh+hl) 2h(l+b) l * b * h Cube 6a 6a2 4a2 a3 Cylinder - 2 π r(r+h) 2πrh π r2 h Cone - π r(r+l) π r l 1/3 (π r2 h) Sphere - 4 π r2 4π r2 4/3 (π r3) Hemisphere - 3 π r2 2 π r2 2/3 (π r3)

## Why Choose Vedantu?

• Provides quick, clear summaries of key concepts.

• Simplifies complex topics for better understanding.

• Efficient tool for last-minute exam prep.

• Enhances retention of crucial information.

• Supports effective exam preparation with key points and tips.

• Saves time by consolidating information.

• Prioritizes important topics and questions.

• Offers practical examples for real-world connections.

• Boosts student confidence for exams.

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.

### 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.

## 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.

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

1. How the formula of a 3-D regular geometric shape is determined?

If you follow the Surface Areas and Volumes Class 10 notes, you will find out how the features of a 3-D geometric shape are analyzed and then used to determine a formula. Even the curved surface area can be calculated in the same manner.

2. What is the difference between a cube and a cuboid?

A cube is a 3D shape where all the three dimensions are the same whereas a cuboid has different dimensions for length, breadth and height.

3. How can we determine the surface area of a particular side of a shape?

By referring to the Class 10 Maths revision notes Chapter 12, you can easily find out how a particular area of a surface of a geometric shape is determined.

4. What are the main topics covered in Chapter 12 of Class 10 Maths?

The students will get well versed in the topics such as the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, and frustum of a cone. With the help of the revision notes, students will understand the concepts well enough to secure a perfect score in the Class 10 Maths board exam. Download the revision notes on Vedantu’s website and start your exam preparations.

5. What are the key features of revision notes provided by Vedantu for Chapter 12 of Class 10 Maths?

The revision notes prepared by Vedantu are great reference material for the students to prepare for their finals. Since the revision notes are completely prepared based on the updated syllabus the students need not worry about missing out on any concepts. These notes are prepared by an excellent group of Maths tutors and the information provided is accurate and authentic. The language used to explain the problems is very simple and easy to understand. With the help of these revision notes, students can ace their exams. They are free of cost and also available on Vedantu Mobile app.

6. How to score full marks in Chapter 12 of Class 10 Maths using revision notes?

Students can score full marks in Chapter 12 of Class 10 Maths with the help of revision notes provided by Vedantu. Since it is very simple and very easy to comprehend, students can clear all their doubts. When they completely understand and grasp the concept, it will be easier for the students to attend to all the questions in the exams without any fear. The students can practise all the problems given in the revision notes to get well-versed in all the concepts.

7. Where can I download the revision notes for Chapter 12 of Class 10 Maths?

Students can download the revision notes for Chapter 12 of Class 10 Maths in Vedantu. Vedantu has proved to be one of the most trusted online learning spaces for students. They strictly follow the CBSE syllabus and guidelines while preparing these revision notes. A qualified group of experts at Vedantu carefully created these revision notes for the benefit of the students. Downloading these revision notes would be the wise choice for the students aiming to score full marks in this subject.

8. What are the steps to download the revision notes for Chapter 12 of Class 10 Maths and can I view them offline?