Volume of Solids

Volume of Solids

Bodies that occupy space are called solids.
Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone.
The space occupied by a solid body is called its volume.
The units for volume are cubic centimetre(cm³), cubic metre(m³) etc.
A cuboid is a solid bounded by six rectangular plane faces.
Consider a cuboid of length, breadth and height , and , respectively. Then:

• Volume of cuboid = lbh cubic units
• Total surface area of cuboid = 2(lb + bh + lh)sq.units
• Lateral surface area of cuboid = Area of 4 walls = Area of 4 walls = 2h(l + b)sq.units

A cube whose length, breadth and height are all equal is called a cube.
Consider a cube of edge a units. Then:

• Volume of cube = a³ cubic units
• Total surface area of cube = 6a² sq.units
• Lateral surface area of cube = 4a² sq.units

A solid bounded by a cylindrical surface and two parallel circular bases at the top and bottom is called a cylinder.
Consider a cylinder of radius r units and height h units. Then:

• Volume of cylinder
• Total surface area of cylinder
• Lateral surface area of cylinder

The volume of a cylinder is also sometimes known as its capacity.