Surface area and volume class 9 formula sheet | Class 9 maths notes of chapter 13 surface area and volume

Introduction

In this article we will be providing you Important formulas of maths class 9 PDF of chapter 13 surface area and volume and we will also provide you the Class 9 maths notes of chapter 13 surface area and volume.






Topics we are going to cover 

  • Important formulas of maths class 9
  • Important formulas of maths class 9 PDF download link 
  • Class 9 maths notes of chapter 13 surface area and volume 
  • Class 9 maths notes of chapter 13 PDF download link 

Important formulas of maths class 9


CUBOID

Let length = l, breadth = b and height = h. 

Then, we have: 

(i) Volume of cuboid = (l x b xh) cubic units.


(ii) Total surface area of the cuboid=2(lb+bh+lh) sq units.


(iii) Lateral surface area of the cuboid = (2(l+b) × h) sq units.


(iv) Diagonal of the cuboid = {√l²+ b² + h²) units.


CUBE 

Let each edge of the cube be a. Then, we have:


(i) Volume of the cube=a^3cubic units.


(ii) Total surface area of the cube= (6a²) sq units. 

(ii) Lateral surface area of the cube= (4a²) sq units.


(iv) Diagonal of the cube= (a√3) units. 


CYLINDER 

Let the radius of the base be r and height be h. 

Then, we have:


(i) Volume of the cylinder = (πr²h) cubic units. 

(ii) Total surface area of the cylinder = (2πr(r+h)) sq units.


(iii) Curved surface area of the cylinder - (2πrh) sq units.


CONE 

Let the radius of its base be r, height be hand slant height be

Then, we have:


(1) Volume of the cone = (⅓ πr²h) cubic units. 

(ii) Curved surface area of the cone= (πrl) sq units.


(iii) Total surface area of the cone= (πrl+2πr²) sq units.


(iv) Slant height of the cone= √l²+r².


SPHERE 

Let the radius of the sphere be r. 

Then, we have: 

(i) Volume of the sphere = {4/3 πr³} cubic units.


(ii) Surface area of the sphere = (4πr²) sq units.


HEMISPHERE 

Let the radius of the hemisphere be r. 

Then, we have:


(1) Volume of the hemisphere = (2/3πr³) cubic units.


(ii) Curved surface area of the hemisphere = (2πr²) sq units.


(iii) Total surface area of the hemisphere = (3πr²) sq units.


Hope you like the important formulas of surface area and volume class 9. Let us know in comment section.


Important formulas of surface area and volume maths class 9 PDF

 (click on the button)

Important formulas of surface area and volume maths class 9 PDF


Class 9 maths notes of chapter 13 surface area and volume

The surface area and volume chapter 15 for class 9 notes are given here. In this part, all the formulas in the chapter surface area and volume for different 3-D shapes are given with a complete explanation. For any 3-D figure, the surface area can be broadly classified into the following three categories Curved Surface Area(CSA), Lateral Surface Area (LSA), and Total Surface Area (TSA). These can be computed for 3d shapes such as a cube, cuboid, cone, cylinder and so on.

Students will be introduced to the surface areas and volumes for different 3-D shapes such as cuboid, cube, right circular cylinder, right circular cone, sphere and hemisphere
Let us see the important notes and formulas for each of the shapes.

Cuboid

A cuboid is a 3-D Shape. The cuboid is made from six rectangular faces, which are placed at adjacent to each other at right angles. 

Total Surface Area of a Cuboid

The total surface area of a cuboid is equal to the sum of the areas of its six rectangular faces.

Surface area and volume notes



Consider a cuboid whose length is “l” cm,
breadth is "b" cm and height "h" cm.
Area of face ABCD = Area of Face EFGH (× bcm2
Area of face AEHD = Area of face BFGC (× hcm2
Area of face ABFE = Area of face DHGC (× hcm2
Total surface area (TSA) of cuboid = Sum of the areas of all its six faces
2(× b2(× h2(× h)
TSA (cuboid)= 2(lb + bh +lh)

Lateral Surface Area of a Cuboid
Lateral surface area (LSA) is the area of all the sides apart from the top and bottom faces{Area of four walls}.
The lateral surface area of the cuboid
= Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC
2(× h2(× h)
LSA (cuboid) = 2(l + b)h Or  perimeter × h

Cube

cuboid whose length, breadth and height all are equal, is known as cube. It is a 3-D shape bounded by six equal squares. It has 12 edges ,12 faces and 8 vertices.
Total Surface Area of a Cube
The total surface area of a cube is equal to the sum of the areas of its six square faces.
                                                                                                                                                                             
Surface area and volume notes

Suppose the length of a side of the cube is a,
The area of one of the six squares = a²
The area of six squares (Total Surface Area)= 6a²

Lateral Surface Area Of a Cube

the lateral surface area of a cube is equal to the area of all the faces except the top and the bottom one .
in other word we can also say that it is the area of four walls of a cube .

Since, the area of one face = a²
the area of four walls (lateral surface area ) = 4a²

Right Circular Cylinder

A right circular cylinder is a closed 3-D solid that has two parallel circular bases connected to each other by a curved surface in which the two bases are exactly over each other and their axis is at right angles to the base . hence, it is known as right circular cylinder.

Lateral Surface Area Of a Right Circular Cylinder

So, if we take a cylinder of base radius r and height h, and open it's curved curved surface to form a rectangle then its breadth would be the circumference of the base i.e. 2πr and length of the rectangle would be the height of the cylinder.

Surface area and volume notes





So, the area of the rectangle (the latral surface area of the cylinder)= l×b
                                                                                                                 =h× 2πr =  2πrh

Total Surface Area Of a Right Circular Cylinder
the Total Surface Area of a right circular cylinder = (lateral surface area) + (area of two bases)
                                                                                2πrh + 2(πr²)
                                                                                2πrh + 2πr²
  2πr(h+r)

Right Circular Cone


A right circular cone is a circular cone whose axis is fixed perpendicular to its base.
Surface area and volume notes


It is formed when a right triangle is revolved around any of its arms .

What is the relation between slant height and height of a right circular cone

The relationship between slant height(l) and height(h) of a right circular cone is:
l² = h² + r² (Using Pythagoras Theorem since l is the hypotenuse and r and h its arms)
Where r is the radius of the base of the cone.

Lateral surface area of a right circular cone

Suppose a right circular cone with slant hieght l and base radius r 

So if we move radius along the the circumference of the base with on of its point fixed at at the vertice it will cover the curved surface area
So. The radius =r
Slant height=l

The lateral surface area=(2πr)×l
                                           =πrl
Total Surface area of a right circular cone

Lateral surface area of cone + area of the circular base
πrl+πr²= πr(l+r)

Sphere

A sphere is a closed three-dimensional solid figure, where all the points on the surface of the sphere are equidistant from the common fixed point called “centre”. The equidistant is called the “radius”.

Surface area of a sphere 

Surface area of a sphere is 4 times the area of a circle i.e.  4×πr²
For a sphere the total surface area=the curved surface area.

Volume and capacity

Volume is the space occupied by the the matter and capacity is the amount of matter that can be accommodated in the object 
To find the capacity in litres here are some important formulaes:-

1000 l = 1m³
1000 cm³ = 1 l
1 ml = 1cm³

FAQ (frequently asked questions)

Question 
What are the formulas of surface area and volume?

Answer
All the formulas that are used in the chapter surface area and volumes are provided on edugyane.in with thier download link.


Question
What is the easiest way to learn surface area and volume formulas Class 9?

Answer
The easiest way to learn formale is to practice multiple formulae based questions and write the formulae multiple times in your notebook or where ever you want.

Question
How do you calculate Class 9 volume?

Answer
You can calculate the volume of any 3-D figure by applying it's respective formulaes

  • Volume of cuboid = (l x b xh) cubic units
  • Volume of the cube=a^3cubic units
  • Volume of the cylinder = (πr²h) cubic units
  • Volume of the cone = (⅓ πr²h) cubic units 
  • Volume of the sphere = {4/3 πr³} cubic units
  • Volume of the hemisphere = (2/3πr³) cubic units

Question 
What is the name of chapter 13 Class 9 maths? 

Answer
SURFACE AREAS AND VOLUMES is the name of chapter 13 class 9 maths.

Also read 


Conclusion

Hope you like the Important formulas of maths class 9 PDF and Class 9 maths notes of chapter 13 surface area and volume. Let us know in comment section.

0 Comments

If you have any doubt or need any study material comment.

Post a Comment

If you have any doubt or need any study material comment.

Post a Comment (0)

Previous Post Next Post