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.
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Important formulas of surface area and volume maths class 9 PDF
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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.
Consider a cuboid whose length is “l” cm,
breadth is "b" cm and height "h" cm.
Area of face ABCD = Area of Face EFGH = (l × b) cm2
Area of face AEHD = Area of face BFGC = (b × h) cm2
Area of face ABFE = Area of face DHGC = (l × h) cm2
Total surface area (TSA) of cuboid = Sum of the areas of all its six faces
= 2(l × b) + 2(b × h) + 2(l × h)
TSA (cuboid)= 2(lb + bh +lh)
Area of face AEHD = Area of face BFGC = (b × h) cm2
Area of face ABFE = Area of face DHGC = (l × h) cm2
Total surface area (TSA) of cuboid = Sum of the areas of all its six faces
= 2(l × b) + 2(b × h) + 2(l × 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(b × h) + 2(l × h)
LSA (cuboid) = 2(l + b)h Or perimeter × h
The lateral surface area of the cuboid
= Area of face AEHD + Area of face BFGC + Area of face ABFE + Area of face DHGC
= 2(b × h) + 2(l × h)
LSA (cuboid) = 2(l + b)h Or perimeter × h
Cube
A 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. 
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.
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.
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.
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Conclusion
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