Volume of a Hexagonal Pyramid

The volume of a hexagonal pyramid is the space it occupies in a 3-dimensional plane. It is the capacity of a hexagonal pyramid or the number of unit cubes that can be fit into it. The volume is expressed in cubic units such as m³, cm³, mm³, and in³.

Formula

The formula is:

Let us solve some examples to understand the concept better.

Solved Examples

Find the volume of a hexagonal pyramid with a base of 5 cm, and a height of 8.5 cm.

Solution:

As we know,
Volume (V) = ${\dfrac{\sqrt{3}}{2}b^{2}h}$, here b = 5 cm and h = 8.5 cm
∴ V = ${\dfrac{\sqrt{3}}{2}\times 5^{2}\times 8\cdot 5}$
= 184.03 cm³ 

Find the volume of a hexagonal pyramid with a base of 8 cm, an apothem of 6.93 cm, and a height of 13 cm.

Solution:

Here, we will use an alternative formula.
Volume (V) = abh, here a = 6.93 cm, b = 8 cm, h = 13 cm
∴ V = 6.93 × 8 × 13
= 720.72 cm³