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# Surface Areas and Volumes Class 9 Notes CBSE Maths Chapter 13 (Free PDF Download)

Last updated date: 15th Jul 2024
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## Class 9 Maths Revision Notes for Surface Areas and Volumes of Chapter 13 - Free PDF Download

Free PDF download of Class 9 Maths revision notes & short key-notes for Surface Areas and Volumes of Chapter 13 to score high marks in exams, prepared by expert mathematics teachers from the latest edition of CBSE books. Register Online for Class 9 Science tuition on Vedantu.com to score more marks in your examination. Vedantu is a platform that provides free CBSE Solutions (NCERT) and other study materials for students. Maths Students who are looking for better solutions can download Class 9 Maths NCERT Solutions to help you to revise the complete syllabus and score more marks in your examinations.

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## Access Class 9 Maths Chapter 13 – Surface Areas and Volumes Notes

### Solids:

Any object occupying fixed space and volume is called a solid.

For example: cube, cuboid, sphere, cylinder, cone etc.

1. Surface Area of a Solid:

The area occupied by a solid object is known as surface area.

The unit of surface area is taken as square unit.

Example- square meter$({{m}^{2}})$.

2. Volume of a Solid:

The measure of the occupied space is called volume of a solid.

The unit of volume is cubic unit.

Example- cubic meter$({{m}^{3}})$

### Formulas for Different Solids:

1. Cuboid

A three-dimensional solid having six rectangular faces is called a cuboid. A cuboid has 6 rectangular faces, 12 edges and 8 vertices with opposite faces of equal dimensions.

The example of a cuboid is a book, matchbox, shoebox etc.

Surface Area of Cuboid:

$S=2(lb+bh+lh)$

Where $l$ is length, $b$ is breadth and $h$ is the height of the cuboid.

Volume of Cuboid:

$V=l\times b\times h$

Where $l$ is length, $b$ is breadth and $h$ is the height of the cuboid.

2. Cube

A cuboid having equal length, breadth and height is called a cube.

For example- ice cubes, dice etc.

Surface Area of Cube:

$S=6{{l}^{2}}$

Where $l$ is length of each side of the cube.

Volume of Cube:

$V={{l}^{3}}$

Where $l$ is length of each side of the cube.

3. Cylinders

A solid generated by stacking large number of circular discs along their diameter on top of the other is called a cylinder. For example, circular pillars, circular pipes, measuring cylinders, soft drink cans etc.

Hollow Cylinder

Solids like iron pipes, rubber tubes, etc., are in the shape of hollow cylinders.

Surface Area of Cylinder:

a) Curved surface area (CSA): $CSA=2\pi rh$

b) Total Surface area (TSA): $TSA=2\pi r(r+h)$

Where $r$ is radius of circular top and bottom and $h$ is the height of cylinder.

Volume of Cylinder:

$V=\pi {{r}^{2}}h$

Where $r$ is radius of circular top and bottom and $h$ is the height of cylinder.

4. Right Circular Cone

The solid generated by the rotation of a right-angled triangle about a right-angled side is called a right circular cone.

Surface Area of Cone:

a) Curved Surface Area (CSA): $CSA=\pi rl$

b) Total Surface Area (TSA): $TSA=\pi r(r+l)$

Where $r$ is radius of circular part, $h$ is the perpendicular height and $l=\sqrt{{{r}^{2}}+{{h}^{2}}}$ is the slant height of the cone.

Volume of Cone:

$V=\dfrac{1}{3}\pi {{r}^{2}}h$

Where $r$ is radius of circular part, $h$ is the perpendicular height of  the cone.

5. Sphere

The three-dimensional solid obtained from collection of all the points in space lying at the constant distance called as radius, from the fixed point called centre, is known as sphere.

For example- a bowling ball, cricket ball etc.

Surface Area of Sphere:

$SA=4\pi {{r}^{2}}$

Where $r$ is the radius of sphere.

Volume of Sphere:

$V=\dfrac{4}{3}\pi {{r}^{3}}$

Where $r$ is the radius of the sphere.

1. Spherical Shell

The solid region between two hollow concentric spheres of different radius.

For example- a ping pong ball, football etc.

Surface Area of Shell:

$SA=4\pi {{R}^{2}}$

Where $R$ is the radius of the outer sphere.

Volume of Solid Part of Shell:

$V=\dfrac{4}{3}\pi ({{R}^{3}}-{{r}^{3}})$

Where $R$ is the radius of outer sphere and $r$ is the radius of the inner sphere.

2. Hemisphere

When a plane slices a solid it into two equal parts, passing through the centre, then each part is called a hemisphere.

For example: A dome shaped roof of a building, ball sliced into equal parts etc.

Surface Area of Hemisphere:

a) Curved Surface Area (CSA): $CSA=2\pi {{r}^{2}}$

b) Total Surface Area (TSA): $TSA=3\pi {{r}^{2}}$

Where $r$ is radius of the circular region.

Volume of Hemisphere:

$V=\dfrac{2}{3}\pi {{r}^{3}}$

Where $r$ is the radius of the hemisphere.

## CBSE Class 9 Maths Notes Chapter 13 Surface Areas and Volumes PDF

CBSE Class 9 Chapter 13 Surface Areas and Volumes contains 9 exercises, starting from 13.1 to 13.9. The solutions to these exercises are available below:

• Exercise 13.1: 8 questions

• Exercise 13.2: 11 questions

• Exercise 13.3: 8 questions

• Exercise 13.4, 13.5 and 13.7: 9 questions each

• Exercise 13.6: 8 questions

• Exercise 13.8: 10 questions

• Exercise 13.9: 3 questions

Notes to these exercises are prepared as per the latest CBSE guidelines for the session 2024-25 and they are available on our website in PDF format for free.

Revision Notes Class 9 Maths Chapter 13 provided by Vedantu helps students revise each and every important concept related to Surface Areas and Volumes in detail.

### Importance of CBSE Class 9 Maths Revision Notes

• CBSE revision notes on class 9 Surface Areas and Volumes will provide you with a summary of all the important and relevant topics as well as highlight the significant references from the Surface Areas and Volumes Class 9 Notes.

• Notes of class 9 revision notes chapter 13 will provide you with a summary of all the important and relevant topics as well as highlight the significant references from chapter 13 Simple Surface Areas and Volumes.

### Let Us Revise Some Important Concepts and Formulas of Surface Areas and Volumes.

1. Surface Area

The surface area is the area taken by the three-dimensional object. As the three-dimensional object is made up of 2D faces, so surface area is the sum of the areas of all the faces of that object.

The surface area can be classified as:

• Curved Surface Area (CSA).

• Lateral Surface Area (LSA)

• Total Surface Area (TSA)

2. Volume

The space occupied by any 3-D object is the volume of that object. The volume of a solid shape is the product of three dimensions, so we express the volume as cubic units.

3. Important Formulas for Surface Areas and Volumes

Formulas for LSA/ CSA, TSA, and Volume related to 3d Shapes (Solid shapes)

### Surface Area and Volume Formula in a Tabular Form are Given Below

 S.no Name Abbreviations Used Lateral /Curved Surface Area Total Surface Area Volume 1. Cuboid H=height,l=length  b=breadth 2h(l+b) 6l2 L * b* h 2. Cube a=length of the sides 4a2 6a2 a3 3. Right Prism .. Perimeter of Base×Height Lateral Surface Area+2(Area of One End) Area of Base×Height 4. Right Circular Cylinder r=radiush=height 2 (π × r × h) 2πr (r + h) πr2h 5. Right pyramid .. ½ (Perimeter of Base×Slant Height) Lateral Surface Area+Area of the Base ⅓ (Area of the Base)×Height 6. Right Circular Cone r=radiusl=length πrl πr (l + r) ⅓ (πr2h) 7. Sphere r=radius 4πr2 4πr2 4/3πr3 8. Hemisphere r=radius 2πr2 3πr2 ⅔ (πr3)

The students can go through these Vedantu Class 9 Maths Notes of Surface Area and Volumes PDF to excel with highest scores in the CBSE Class 9 examination.

The Maths experts at Vedantu prepared the CBSE Class 9 Maths Revision Notes. Every step and concept is explained clearly in the answers provided by Vedantu. Class 9 Maths Notes of Surface Area and Volumes PDF provided by Vedantu help students revise each and every important concept related to Surface Area and Volumes in detail.

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## Conclusion

Vedantu's CBSE Class 9 Maths Chapter 13 Revision Notes are a valuable resource for students who want to gain a sound knowledge in the concepts of surface areas and volumes and to perform their best in their exams. These revision notes are comprehensive, aligned with the latest CBSE syllabus and NCERT guidelines, and written in a clear and concise style that is easy to understand. They include a variety of solved and unsolved problems to practice with, and they are prepared by experienced teaching faculties and subject matter experts.

## FAQs on Surface Areas and Volumes Class 9 Notes CBSE Maths Chapter 13 (Free PDF Download)

1. What is surface area and volume Class 9?

Surface area is the total area of all the faces of a solid object, while volume is the amount of space that a solid object occupies.

2. What is the formula for surface area and volume?

Surface area:

• Cube: 6a²

• Cuboid: 2(lb + bh + lh)

• Cylinder: 2πrh + 2πr²

• Cone: πr(r + l)

• Sphere: 4πr²

Volume:

• Cube: a³

• Cuboid: lbh

• Cylinder: πr²h

• Cone: ⅓πr²h

• Sphere: 4/3πr³

Note that these are just the basic formulas for surface area and volume. There are more complex formulas for other shapes and solids.

3. What is the formula of area?

Rectangle: Area = length × width

• Square: Area = side × side

• Triangle: Area = 1/2 × base × height

• Circle: Area = π × radius²

4. What is the formula of volume used for?

Volume is an important concept in mathematics and physics, and it has many real-world applications. For example, volume is used to calculate the amount of water in a swimming pool, the amount of air in a balloon, and the amount of concrete required to build a foundation.

5. How to remember formulas of surface area and volume class 9?