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Last modified on August 3rd, 2023

The volume of a pentagonal pyramid is the space it occupies in a 3-dimensional plane. It is the capacity of a pentagonal 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 is:

The formula to calculate the volume of a right and the non-right pentagonal pyramid is the same s as only its perpendicular height is considered irrespective of the position of the apex.

Let us solve some examples to understand the concept better.

**Find the volume of a pentagonal pyramid with a base length of 11 cm, an apothem of 7.57 cm, and a height of 16 cm.**

Solution:

As we know,

Volume (V) = ${\dfrac{5}{6}abh}$, here a = 7.57 cm, b = 11 cm, h = 16 cm

∴ *V* = ${\dfrac{5}{6}\times 7.57\times 11\times 16}$

= 1110.26 cm^{3}

**Find the volume of a right pentagonal pyramid with a base length of 16 mm, an apothem of 11.01 mm, and a height of 19 mm.**

Solution:

As we know,

Volume (V) = ${\dfrac{5}{6}abh}$, here a = 11.01 cm, b = 16 cm, h = 19 cm

∴ *V* = ${\dfrac{5}{6}\times 11.01\times 16\times 19}$

= 2789.2 mm^{3}

Finding the volume of a pentagonal pyramid when the **BASE** and **HEIGHT** are known

**Find the volume of a pentagonal pyramid with a height of 9.8 cm, and a base of 7 cm.**

Solution:

Here we will use an alternative formula to calculate the volume.

Volume (V) = ${\dfrac{1.72}{3}b^{2}h}$, here b =7 cm, h = 9.8 cm

∴ V = ${\dfrac{1.72}{3}\times 7^{2}\times 9.8}$

= 275.31 cm^{3}

Last modified on August 3rd, 2023