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

Definitions:

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.

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• 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

Download Surface Area and Volumes Notes PDF

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