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