# Volume of a Triangular Pyramid

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

## Formulas

The formula is:

Let us solve some examples to understand the concept better.

## Solved Examples

Find the volume of a triangular pyramid with a base area of 60 cm2, and height is 18 cm.

Solution:

As we know,
Volume (V) = ${\dfrac{1}{3}Bh}$, here B = 60 cm2, h = 18 cm
V = ${\dfrac{1}{3}\times 60\times 18}$
= 360 cm3

Find the volume of a pyramid with a triangular base of side length measuring 6 cm, a base height of 5 cm, and a height of 7.2 cm.

Solution:

Since, Volume (V) = ${\dfrac{1}{3}Bh}$,
And,
B = ${\dfrac {1}{2}bH}$, here b = base, H = base height,
∴ We can write the formula
Volume (V) = ${\dfrac{1}{6}bHh}$, here b = 6 cm, H = 5 cm, h = 7.2 cm
V = ${\dfrac{1}{6}\times 6\times 5\times 7.2}$
= 36 cm3

Find the volume of a right triangular pyramid with a base of 7 cm and a height of 18 cm.

Solution:

As we know,
Volume (V) =  ${ \dfrac{\sqrt{3}}{12}b^{2}h }$, here b = 7 cm, h = 18 cm
V = ${\dfrac{\sqrt{3}}{12}\times 7^{2}\times 18}$
= 127.3 cm3

Finding the volume of a regular (equilateral) triangular pyramid when the BASE and HEIGHT are known

Find the volume of a regular triangular pyramid with a base of 9 cm and a height of 15 cm.

Solution:

Here, we will use an alternative formula for a regular triangular pyramid.
Volume (V) =  ${ \dfrac{\sqrt{3}}{12}b^{2}h }$, here b = 9 cm, h = 15 cm
V = ${\dfrac{\sqrt{3}}{12}\times 9^{2}\times 15}$
= 175.4 cm3