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CBSE Surface Areas and Volumes Class 9th Formulas

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Solids

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.

Cuboid:

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

Examples:

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 .

Remember:

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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