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Last modified on September 6th, 2022

The volume of a rectangular pyramid is the space it occupies in a 3-dimensional plane. It is the capacity of a rectangular pyramid or the number of unit cubes that can be fit into it. The volume is expressed in cubic units such as m^{3}, cm^{3}, mm^{3}, and in^{3}.

The formula to calculate the volume of an oblique or a right rectangular pyramid is the same as we consider the perpendicular height of the pyramid for both cases. The general formula to calculate the volume of a rectangular pyramid is:

**Volume ( V) = ${\dfrac{1}{3}Bh}$**, here B = base area, h = height

The specific formula is given below:

Let us solve some examples to understand the above concept better.

**Find the volume of a rectangular pyramid with a base length of 15 cm, a base width of 9 cm, and a height of 21 cm.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{1}{3}lwh}$, here l = 15 cm, w = 9 cm, h = 21 cm

∴ *V* = ${\dfrac{1}{3}\times 15\times 9\times 21}$

= 945 cm^{3}

**Find the volume of a right rectangular pyramid given in the figure.**

Solution:

As we know,

Volume (*V*) = ${\dfrac{1}{3}lwh}$, here l = 25 cm, w = 17 cm, h = 12 cm

∴ *V* = ${\dfrac{1}{3}\times 25\times 17\times 12}$

= 1700 cm^{3}

Let us learn to calculate the volume of a truncated rectangular pyramid pond by solving an example.

Finding the volume of a truncated rectangular pyramid when **BOTTOM BASE LENGTH**, **BOTTOM BASE WIDTH**, **TOP BASE LENGTH**, **TOP BASE WIDTH**, and **HEIGHT** are known

**Find the volume of a truncated rectangular pyramid pond given in the figure.**

Solution:

Here, we will use the volume formula of truncated rectangular pyramid.

Volume (V) = ${\dfrac{Ab+aB+2\left( ab+AB\right) }{6}\times h}$, here A = 18 m, B = 16 m, a = 9 m, b = 8 m, h = 10 m

∴ *V* = ${\dfrac{18\times 8+9\times 16+2\left( 9\times 8+18\times 16\right) }{6}\times 10}$

= 1680 m^{3}

Last modified on September 6th, 2022