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CBSE Surface Areas and Volumes Class 9th Formulas

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Bodies occupying space are called solids. A solid has three dimensions viz., length, breadth and thickness or depth or height.

The space occupied by a solid body is called its volume .Volume is measured  in  cubic units.

Cuboid and Cube

We shall now study two solid figures which are generated by rectangles and squares respectively.


 A solid bounded by six rectangular faces is called a cuboid.


A match box, a chalk box, a room, a brick etc.

Cube : A cuboid whose length, breadth and height are all equal is called a cube. Dice, ice- cubes, sugar cubes, etc. are all examples of cube. Each edge of a cube is called its side. In figure alongside PQRSTUVW is a cube.

The side or edge of the cube is denoted by letter symbol ‘a’.

Surface area of cuboid = 2[lb + bh + hl] sq. units

Surface area of cube = 6(edge)2 = 6a2sq.units

• Lateral Surface Area : Later surface area of a cuboid is the sum of areas of four faces leaving the top face and bottom face.

Lateral surface area of the cuboid : 2[l+b]×h sq. units

Lateral surface area of the cube = 4(edge)2 = 4a2 sq units .


Right Circular Cylinder

Solids like measuring jars, circular pillars, circular pipes, road rollers etc. are said to have a cylindrical shape.

A solid generated by revolving a rectangle about one of its sides is called circular cylinder .

Let ABCD be a rectangle , which revolves about its side AB and completes a full round to arrive at its initial position .This revolution generates a right circular cyclinder as shown in the figure . AB is called the axis of the cyclinder .The length AB is the length or the height of the cyclinder, AD = BC is called its radius .

There is another way of obtaining a right circular cylinder. If we take a number of circular sheets of cardboard and stack them up vertically.

1. Volume of cylinder = πr2h

2. Total surface area of a cylinder = 2πr(r+h)

3. Curved surface area of a cylinder = 2πrh

where r is radius of the base and h is the height of the cylinder.

Right Circular Cone

In our day to day life we come across many objects like a birthday cap (worn by children), a  mehandi cone, an ice-cream cone etc. These peculiar shapes as the one shown in figure is known as right circular cone.

The solid generated by the rotation of a right angled triangle about one of the sides containing the right angle is called a right circular cone. Thus, when a right-angled triangle VOA is revolved about OV, it generates a cone shown in figure alongside.

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• Sphere and Hemisphere

• For  a sphere of radius r, we have :

Surface area = 4πr2

Volume = 4/3 πr3

• For a hemisphere of radius r, we

Curved surface area = 2πr2

Total surface area = 3 πr2

Volume of hemisphere = 2/3 πr3

• For volume of hemisphere shell of external and internal radii R and r respectively is 2/3 π(R3-r3).

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