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Volume of Solids

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Volume of Solids - Lesson Summary

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 are l,b and h respectively.

     •  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 = 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.

     •  Volume of cube = a 3 cubic units

     •  Total surface area of cube = 6a 2 sq.units

     •  Lateral surface area of cube = 4a 2 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.

     •  Volume of cylinder = πr 2h cubic units

     •  Total surface area of cylinder = 2πr( r + h) sq.units

     •  Lateral surface area of cylinder = 2πrh 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 = π(R 2 - r 2) sq.units

Curved surface area (CSA) = 2πh(R + r) sq.units

Total surface area (TSA) = 2π(R + r)(h + R - r) sq.units, where R = external radius, r = internal radius and h = height.

Volume (V) = πh(R 2 - r 2) cubic units.


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