The volume of a prism is the total amount of space it occupies in the three-dimensional plane. It is measured in cubic units, such as cm3, m3, in3, ft3, yd3.
Formulas
The general formula to find the volume of any prism is:
Volume (V) = Base Area × Height, here, the height of any prism is the distance between the two bases.
However, there are specific formulas to calculate the volume of different prisms due to their different shapes.
They are given below:
Volume of a Prism
Some formulas have additional labeling for particular prisms.
In triangular, rectangular, and trapezoidal prisms, ‘l’ (or length) stands for the distance between the bases, and ‘h’ stands for the height of the polygonal base. ‘l’ is the length for a square prism, and ‘a’ represents the four congruent base edges. For pentagonal and hexagonal prisms, ‘a‘ is the apothem, and ‘b’ is the base edge.
Let us solve some examples involving the above formulas to understand the concept better.
Solved Examples
Find the volume of a triangular prism whose base is 40 cm, height is 15 cm, and length is 60 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{2}\times b\times h\times l}$, here b = 40 cm, h = 15 cm, l = 60 cm ∴ V = ${\dfrac{1}{2}\times 40\times 15\times 60}$ = 18000 cm3
Find the volume of a rectangular prism whose width is 7 cm, height is 12 cm, and length is 16 cm.
Solution:
As we know, Volume (V) = l × w × h, here l = 16 cm, w = 7 cm, h = 12 cm ∴ V = 16 × 7 × 12 = 1344 cm3
Find the volume of a pentagonal prism whose base is 6 cm, apothem is 4.13 cm, and height is 8 cm.
Solution:
As we know, Volume (V) = ${\dfrac{5}{2}abh}$, here a = 4.13 cm, b = 6 cm, h = 8 cm ∴V = ${\dfrac{5}{2}\times 4.13\times 6\times 8}$ = 495.6 cm³
Find the volume of a hexagonal prism whose base is 12 cm, apothem is 10.39 cm and height is 20 cm.
Solution:
As we know, Volume (V) = 3abh, here a = 10.39 cm, b = 12 cm, h = 20 cm ∴V = 3 × 10.39 × 12 ×20 ≈ 7480.8 cm³
Find the volume of a trapezoidal prism whose base edges are 34 cm, and 22 cm, and vertical height is 12 cm, and length is 52 cm.
Solution:
As we know, Volume (V) = ${\dfrac{1}{2}\left( a+b\right) \times h\times l}$, here a = 34 cm, b = 22 cm, h = 12 cm, l = 52 cm ∴V = ${\dfrac{1}{2}\times \left( 34+22\right) \times 12\times 52}$ = 17472 cm3
Find the volume of a square prism whose base edge is 7 in, and length is 11 in.
Solution:
As we know, Volume (V) = a2× l, here a = 7 in, l = 11 in ∴V = 72 × 11 = 539 in3
