3.7.1 Volume

Volume is the amount of space that an object occupies or the amount of space that is enclosed within the boundaries of an object.

• It is typically measured in cubic units, such as cubic meters or cubic feet.

• Volume can refer to the three-dimensional size of a solid object, like a cube or sphere, or the amount of space occupied by a liquid or gas.

The method for calculating the volume of an object depends on its shape. Here are some common shapes and their respective volume formulas:

• Rectangular Prism:

• The volume of a rectangular prism can be calculated by multiplying its length, width, and height.

• The formula is

\( V=l\times w\times h \)

where \( V \) represents the volume, \( l \) represents the length, \( w \) represents the width, and \( h \) represents the height.

• Triangular Prism:

• The volume of a triangular prism can be calculated by multiplying the area of the triangular base by the height of the prism.

• The formula is:

\( V =\frac{1}{2}\times b\times h\times l \)

where \( V \) represents the volume, \( b \) represents the base of the triangular base, \( h \) represents the height of the triangular base, and \( l \) represents the length of the prism.

• To use this formula, first, calculate the area of the triangular base by multiplying its base by its height and dividing the result by \( 2 \).

• Then, multiply this area by the length of the prism.

• Cube:

• The volume of a cube is calculated by multiplying the length of any one side by itself three times.

• The formula is \( V=s\times s \times s=s^3 \)

where\( V \) represents the volume, and s represents the length of one side.

• Sphere:

• The volume of a sphere can be calculated by using the formula

\( V=\frac{4}{3}r^3 \)

where \( V \) represents the volume, represents the mathematical constant pi (approximately \( 3.14 \) ), and \( r \) represents the radius of the sphere.

• Cylinder:

• The volume of a cylinder is calculated by multiplying the area of the base by the height.

• The formula is \( V =\pi r^2×h \)

where \( V \) represents the volume, represents the mathematical constant pi, \( r \) represents the radius of the base, and \( h \) represents the height of the cylinder.

• Cone:

• The volume of a cone can be calculated by using the formula

\( V=\frac{1}{3}r^2\times h \)

where \( V \) represents the volume, represents the mathematical constant pi, \( r \) represents the radius of the base, and h represents the height of the cone.

These are just a few examples, but there are many more formulas for calculating the volumes of different shapes.

Worked example:

\( ABCDEFGH \) is a cuboid.

\( AB=8 \) cm, \( BC=5 \) cm and \( CG=11 \) cm.

Work out the volume of cuboid.

Volume of a cuboid is given by

\( V=l\times w \times h \)

Here length is \( 8 \) cm, width is \( 5 \) cm and height are \( 11 \) cm.

Put these values in the formula

\( V=8\times 5 \times 11 \)

\( V=440 \)

\( V=440 cm^3 \)