Table of Contents

Last modified on August 3rd, 2023

chapter outline

 

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:

Volume of a Triangular Pyramid

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

Last modified on August 3rd, 2023

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