Volume of a Pyramid Formula

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle called a lateral face. The volume of a pyramid is the measure of the number of units occupied by the pyramid.

Volume of a Pyramid Formula

The Volume of a Pyramid Formula is given as,

\[\large Volume\;of\;a\;square\;pyramid=\frac{1}{3}b^{2}h\]

\[\large Volume\;of\;a\;triangular\;pyramid=\frac{1}{6}abh\]

\[\large Volume\;of\;a\;pentagonal\;pyramid=\frac{5}{6}abh\]

\[\large Volume\;of\;a\;hexagonal\;pyramid=abh\]

a – apothem length of the pyramid
b – base length of the pyramid
h – height of the pyramid

Volume of a Pyramid Formula Solved Example

Example: A pyramid has a square base of side 4 cm and a height of 9 cm. Find its volume.


b = 4 cm
h = 9 cm

\(\begin{array}{l}V=\frac{1}{3}b^{2}h\end{array} \)

\(\begin{array}{l}=\frac{1}{3}\times4^{2}\times9\end{array} \)

\(\begin{array}{l}=48\end{array} \)

So, the volume is

\(\begin{array}{l}48\,cm^{3}\end{array} \)

More topics in Volume of a Pyramid Formula
Volume of a Square Pyramid Formula

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