Volume of Solids
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Volume of Solids
Solids: Bodies that occupy space are called solids. Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone. Volume: The space occupied by a solid body is called its volume. The units for volume are cubic centimetre(cm3), cubic metre(m3) etc. Cuboid: A cuboid is a solid bounded by six rectangular plane faces. Consider a cuboid of length, breadth and height are l,b and h respectively.      â€¢  Volume of cuboid = lbh cubic units      â€¢  Total surface area of cuboid = 2(lb + bh + lh)sq.units      â€¢  Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units Cube: A cube whose length, breadth and height are all equal is called a cube. Consider a cube of edge a units.      â€¢  Volume of cube = a3 cubic units      â€¢  Total surface area of cube = 6a2 sq.units      â€¢  Lateral surface area of cube = 4a2 sq.units Cylinder: 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.      â€¢  Volume of cylinder = Ï€r2h cubic units      â€¢  Total surface area of cylinder = 2Ï€r( r + h) sq.units      â€¢  Lateral surface area of cylinder = 2Ï€rh sq.units. The volume of a cylinder is also sometimes known as its capacity. Hollow cylinder A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder. Surface area of each base = Ï€(R2 - r2) sq.units Curved surface area (CSA) = 2Ï€h(R + r) sq.units Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height. Volume (V) = Ï€h(R2 - r2) cubic units.

#### SUMMARY

Solids: Bodies that occupy space are called solids. Solid bodies occur in various shapes, such as cuboid, cube, cylinder and cone. Volume: The space occupied by a solid body is called its volume. The units for volume are cubic centimetre(cm3), cubic metre(m3) etc. Cuboid: A cuboid is a solid bounded by six rectangular plane faces. Consider a cuboid of length, breadth and height are l,b and h respectively.      â€¢  Volume of cuboid = lbh cubic units      â€¢  Total surface area of cuboid = 2(lb + bh + lh)sq.units      â€¢  Lateral surface area of cuboid = Area of 4 walls = 2h(l + b)sq.units Cube: A cube whose length, breadth and height are all equal is called a cube. Consider a cube of edge a units.      â€¢  Volume of cube = a3 cubic units      â€¢  Total surface area of cube = 6a2 sq.units      â€¢  Lateral surface area of cube = 4a2 sq.units Cylinder: 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.      â€¢  Volume of cylinder = Ï€r2h cubic units      â€¢  Total surface area of cylinder = 2Ï€r( r + h) sq.units      â€¢  Lateral surface area of cylinder = 2Ï€rh sq.units. The volume of a cylinder is also sometimes known as its capacity. Hollow cylinder A solid bounded by two coaxial cylinders of the same height and different radii is called a hollow cylinder. Surface area of each base = Ï€(R2 - r2) sq.units Curved surface area (CSA) = 2Ï€h(R + r) sq.units Total surface area (TSA) = 2Ï€(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height. Volume (V) = Ï€h(R2 - r2) cubic units.

#### REFERENCES

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