The space occupied by an object is called the volume. Volume is three-dimensional. To measure the volumes we need to know the measure of three sides. Since volume involves three sides, so it is measured in cubic units. A surface like the page of a book and a blackboard are called plane surfaces. They do not have any volume but just have an area. The units for volume are cubic centimeters (cm3), cubic meters (m3), etc.
A cube has all sides with equal length.
So, volume of a cube = (side × side × side) cubic units
or,
= (length × length × length) cubic units.
A cuboid is a solid box whose every surface is a rectangle of the same area or different areas. A cuboid has length, breadth, and height.
So, the volume of a cuboid = length × breadth × height = l × b × h cubic 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 = π r2 h cubic units.
The volume of a cylinder is also sometimes known as its capacity.
A sphere is a set of points in space that are given a distance r from the center.
The volume of a sphere = 4 ∕ 3 π r3
The volume of a hemisphere is one-half the volume of the related sphere. So, the volume of a hemisphere = 2 ∕ 3 π r3
Note: The volume of a sphere is 2∕3 of the volume of a cylinder with the same radius, and height equal to the diameter.
A cone is a three-dimensional figure with one circular base. A curved surface connects the base and the vertex.
The volume of a cone with radius r is one-third the area of the base.
V = 1∕3 B × h where B = πr2
or, Volume of a cone = 1∕3 π r2 h
A prism is a polyhedron with two parallel, congruent faces called bases that are polygons. The volume V of a prism is the area of the base B times the height h.
Volume of a prism = B × h
where B is the area of the base and h is the height.
The base of the prism is a rectangle. The area of the base is equal to the length × width.
A pyramid is a polyhedron with one base that is any polygon. Its other faces are triangles.
The volume V of a pyramid is one-third the area of the base B times the height h.
V=1∕3 B × h
where the base of the area (which is a square) = length × length.
Any unit that is used in the measurement of length gives a corresponding unit used in the measurement of volume. Example: a cube’s volume with a given length of the sides can be calculated. A cubic centimeter is the cube’s volume with its sides measuring 1 cm.
The standard unit volume as per the international system units is the cubic meter. Liter is also included in the metric system as a volume unit.
1 liter = 1000 cubic centimeters.
1 cubic metre = 1000 liters.
Several traditional units that have been used in the measurement of volume and which are still in use include board foot, tablespoon, cubic foot, cubic inch, gallon, and barrel among others.
