NCERT Notes for Class 9 Math Chapter 13 Surface Areas and Volumes Notes
Class 9 Maths Chapter 13 Surface Areas and Volumes Notes
Chapter Name  Surface Areas and Volumes Notes 
Class  CBSE Class 9 
Textbook Name  Surface Areas and Volumes Class 9 
Related Readings 

Plane figure
The figures which we can draw on a piece of paper or which lie on a plane are called Plane Figures. Example: Circle, Square, Rectangle etc.Solid figures
The 3D shapes which occupy some space are called Solid Figures. Example: Cube, Cuboid, Sphere etc.
Volume
Space occupied by any solid shape is the capacity or volume of that figure. The unit of volume is a cubic unit.
Surface Area
The area of all the faces of the solid shape is the total surface area of that figure. The unit of surface area is a square unit.
Lateral or Curved Surface Area
The surface area of the solid shape after leaving the top and bottom face of the figure is called the lateral surface of the shape. The unit of lateral surface area is a square unit.
Surface Area and Volume of a Cube
Cube is a solid shape having 6 equal square faces.
Lateral surface area of a cube 
4l^{2} 
Total surface area of a cube 
6l^{2} 
The volume of a cube 
l^{3} 
Diagonal 
√3l, l = edge of the cube 
Example: What is the capacity of a cubical vessel having each side of 8 cm?
Solution
Given side = 8 cm
So, Volume of the cubical vessel = l^{3}
= (8)^{3} = 256 cm^{3} .
Surface Area and volume of a Cuboid
Cuboid is a solid shape having 6 rectangular faces at a right angle.
Lateral surface area of a cuboid 
2h(l + b) 
Total surface area of a cuboid 
2(lb + bh + lh) 
Volume of a cuboid 
lbh 
Diagonal 
l = length, b = breadth, h = height

Example: What is the surface area of a cereal box whose length, breadth and height is 20 cm, 8 cm and 30 cm respectively?
Solution
Given,
Length = 20 cm
Breadth = 8 cm
Height = 30 cm
Total surface area of the cereal box = 2(lb + bh + lh)
= 2(20 × 8 + 8 × 30 + 20 × 30)
= 2(160 + 240 + 600)
= 2(1000) = 2000 cm^{2} .
Surface Area and Volume of a Right Circular Cylinder
If we fold a rectangular sheet with one side as its axis then it forms a cylinder. It is the curved surface of the cylinder. And if this curved surface is covered by two parallel circular bases then it forms a right circular cylinder.
Curved surface area of a Right circular cylinder  2Ï€rh 
Total surface area of a Right circular cylinder  2Ï€r^{2} + 2Ï€rh = 2Ï€r(r + h) 
The volume of a Right circular cylinder  Ï€r^{2} 
r = radius, h = height 
Surface Area and Volume of a Hollow Right Circular Cylinder
If a right circular cylinder is hollow from inside then it has different curved surface and volume.
Curved surface area of a Right circular cylinder 
2Ï€h (R + r) 
Total surface area of a Right circular cylinder 
2Ï€h (R + r) + 2Ï€(R^{2} − r^{2}) 

R = outer radius, r = inner radius 
Example: Find the Total surface area of a hollow cylinder whose length is 22 cm and the external radius is 7 cm with 1 cm thickness. (Ï€ = 22/7)
Solution
Given, h = 22 cm
R = 7 cm
r = 6 cm (thickness of the wall is 1 cm)
Total surface area of a hollow cylinder = 2Ï€h(R + r) + 2Ï€(R^{2} – r^{2} )
= 2(Ï€) (22) (7+6) + 2(Ï€)(7^{2} – 6^{2} )
= 572 Ï€ + 26 Ï€ = 598 Ï€
= 1878.67 cm^{2}
Surface Area and Volume of a Right Circular Cone
If we revolve a rightangled triangle about one of its sides by taking other as its axis then the solid shape formed is known as a Right Circular Cone.
Curved surface area of a Right Circular Cone 

Total surface area of a Right Circular Cone 
Ï€r^{2} + Ï€rl = Ï€r(r + l) 
The volume of Right Circular Cone 
(1/3) Ï€r^{2}h 

r = radius, h = height, l = slant height 
Surface Area and Volume of a Sphere
A sphere is a solid shape which is completely round like a ball. It has the same curved and total surface area.
Curved or Lateral surface area of a Sphere 
4Ï€r^{2} 
Total surface area of a Sphere 
4Ï€r^{2} 
Volume of a Sphere 
(4/3) Ï€r^{3} 

R = radius 
Surface Area and Volume of a Hemisphere
If we cut the sphere in two parts then is said to be a hemisphere.
Curved or Lateral surface area of a Sphere 
2Ï€r^{2} 
Total surface area of a Sphere 
3Ï€r^{2} 
Volume of a Sphere 
(2/3) Ï€r^{3} 

r = radius 
Example: If we have a metal piece of cone shape with volume 523.33 cm3 and we mould it in a sphere then what will be the surface area of that sphere?
Solution
Given, volume of cone = 523.33 cm^{3}
Volume of cone = Volume of Sphere
Volume of sphere = 100 Ï€ cm^{3}
⇒ 125 = r^{3}
⇒ r = 5
Surface area of a sphere = 4Ï€r^{2}
= 314.28 cm^{2} .