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.