Volume of Pyramid with Examples and FAQs

Volume of pyramid

The volume of a pyramid is the total space enclosed by the pyramid. A pyramid is a polyhedron. In a pyramid, the base is a polygon which can be a triangle or square or pentagon, etc., and the lateral sides are triangles that meet at an apex.

Pyramids differ only due to their base. If the base is a triangle it is a triangular pyramid, if it’s a square it’s a square pyramid, if the base is a rectangle then it’s a rectangular pyramid and so on.

The formula for Volume of Pyramid

The general formula of volume of a pyramid whose base area is ‘A’ and the height(altitude) of the pyramid is ‘h’ can be written as:

\text { Volume of Pyramid }=\frac{1}{3} \times \mathrm{A} \times \mathrm{h}

The formula for different types of Pyramids

Examples

Example 1: Find the volume of a square pyramid if the base side is 10 cm in length and the height of the pyramid is 15 cm. 

Solution:

Given length of the side of a square is 10 cm and the height of the pyramid is 15 cm.

We know, Volume of a square pyramid =\frac{1}{3} a^{2} h

where ‘a’ is the length of the side of the square and ‘h’ is the height of the pyramid

\therefore \text { Volume of the given square pyramid }

= \frac{1}{3} \times 10^{2} \times 15 \mathrm{~cm}^{3}

= 100 \times 5 \mathrm{~cm}^{3}=500 \mathrm{~cm}^{3}

Hence the volume of the given pyramid is 500 {~cm}^{3}.

Example 2: A pyramid has a triangle of side length 4 cm and altitude 6 cm as its base and the height of the pyramid is 9 cm. Calculate the volume of the triangular pyramid.

Solution: 

Given that the base triangle has a side length of 4 cm and an altitude of 6 cm.

\therefore \text { Area of Triangle }=\frac{1}{2} \times 4 \times 6=12 \mathrm{~cm}^{2}

= \frac{1}{3} \times \mathrm{A} \times \mathrm{h}

= \frac{1}{3} \times 12 \times 9 \mathrm{~cm}^{3}=36 \mathrm{~cm}^{3}

Therefore, the volume of the pyramid is 36 \mathrm{~cm}^{3}.