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Volume of a Prism

Definition

A prism is a three-dimensional polyhedron resembling a three-dimensional parallelogram. The capacity or the quantity a prism can hold inside it is known as its volume. There are different prism shapes, like rectangular, square, triangular, hexagonal, pentagonal, octagonal, etc. Every prism has its base in different shapes, triangular, hexagonal, square, rectangular, etc. Strictly speaking, a pyramid is not a prism. Prism has identical bases, whereas pyramids have only one identical base.
A prism has identical top and base that are parallel to each other.
The side faces of a prism are flat.
There are no curve sides on a prism.
The prism has the same cross-section along its length.
The volume of a prism is measured in cubic meters, cubic centimeters, cubic feet, etc., and is denoted as m3, cm3, ft3, etc.

Formula for volume of different shapes of prism

Shape

Base

Volume of Prism = Base area × height

Volume formula

Triangular Prism

Triangular

Volume of triangular prism = Area of triangle × height of the prism

Volume of triangular prism = ½ x base x height x length

Square Prism

Square

Volume of square prism = Area of square × height of the prism

Volume of square prism = length x breadth x height

Rectangular Prism

Rectangular

Volume of rectangular prism = Area of rectangle × height of the prism

Volume of rectangular prism = length x breadth x height

Trapezoidal Prism

Trapezoidal

Volume of trapezoidal prism = Area of trapezoid × height of the prism

Volume of trapezoidal prism = Area of trapezoid × height of the prism

Pentagonal Prism

Pentagonal

Volume of pentagonal prism = Area of pentagon × height of the prism

Volume of pentagonal prism = 5/2 x base x height x length 

Hexagonal Prism

Hexagonal

Volume of hexagonal prism = Area of hexagon × height of the prism

Volume of hexagonal prism = 3 x breadth x height x length

Octagonal Prism

Octagonal

Volume of octagonal prism = Area of octagon × height of the prism

Volume of octagonal prism = Area of octagon × height of the prism


Calculation of volume of a prism

We can calculate the volume of a prism by the following steps:
1.) Find the dimensions of the prism.
2.) Determine the shape of the prism and note down the formula from the table above of the specific shape of the prism.
3.) Find the product of the dimensions of the prism and put the relevant units after the numeric value.

Calculation of volume of a prism

Example 1: Find the volume of the prism as shown in the figure.
Solution:

From the given, we can say the shape of the prism is triangular. Therefore, from the triangular prism formula we have,
Volume of the prism = Area of triangle × height of the prism
Area of triangle = ½ x base x height = ½ 12 x 16 = 96 m2.
Volume of the prism = 96 x 20 = 1920 m3.

Example 2: Find the area of the prism whose area is 60 square meters and height is 5 meter.
Solution:

We know the volume of the prism = area x height.
Therefore, the volume of the prism = 60 x 5 = 300 cubic meters.

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