The volume of a rectangular prism is the space it occupies in the three-dimensional plane. It is measured in cubic units such as m3, cm3, mm3, ft3.
Formula
The formula to calculate the volume of a rectangular prism is given below:
Volume of a Rectangular Prism
In the above formula, the product of the length and the width is the base area of the prism. Therefore, we can also write the formula as:
Volume (V) = Base Area x Height
Derivation
The volume of a rectangular prism can be calculated if its base area and height are known.
Let the area of its rectangular faces = A and height = h
Since volume represents the space occupied by the object:
The volume of a rectangular prism = base area × height
⇒ V = B × h …..(i)
Since the base area of a rectangular surface can be written as:
Base area = length × width
⇒B = l × w…..(ii)
Substituting (ii) in (i), we get
V = l × w × h, which is the formula to calculate its volume.
Using Unit Cubes
A cube with sides measuring 1 unit each is known as a unit cube. The volume of a cuboid can also be defined by the number of unit cubes that fit perfectly inside it.
In this case, a rectangular prism is shown, and 12-unit cubes fit perfectly within it.
The volume of each of these unit cubes = l × w × h
= 1 × 1 × 1 = 1 cubic unit
Since the total number of unit cubes = 12
Thus, the volume of the rectangular prism = total number of unit cubes × area of each cube
= 12 × 1 = 12 cubic units.
Solved Examples
Find the volume of a rectangular prism in the figure.
Solution:
As we know, Volume (V) = l × w × h, here l = 12 cm, w = 6 cm, h = 17 cm ∴ V = 12 × 6 × 17 = 1224 cm3
Find the volume of a rectangular prism whose base area is 49 in2 and height is 12 in.
Solution:
As we know, Volume (V) = Base Area x Height, here base Area = 49 in2, w = 6 cm, height = 12 in ∴ V = 49 × 12 = 588 in3
Find the volume of an oblique rectangular prism in the figure.
Solution:
As we know, The volume of an oblique rectangular prism = volume of a right rectangular prism with the same height ‘h’ Volume (V) = l × w × h, here l = 11 cm, w = 9.6 cm, h = 18 cm ∴ V = 11 × 9.6 × 18 = 1900.8 cm3
Find the volume of a rectangular prism in the figure.
Find the volume of an oblique rectangular prism in the figure.