# Volume of a Pentagonal Pyramid

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 m3, cm3, mm3, and in3.

## Formula

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.

## Solved Examples

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 cm3

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 mm3

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 cm3