Volume of a Square Pyramid Formula

Volume of a Square Pyramid

The volume of a pyramid simply refers to the space enclosed between the faces of the pyramid and it is equal to one-third multiplied by the product of base area as well as height. If we talk about a square pyramid, here we know that the base of the pyramid is in the form of a square, thus the formula of volume of square pyramid will change accordingly. Here, we will learn what is the volume of a square pyramid formula and how to calculate it with the help of examples.


Meaning of Square Pyramid

A square pyramid is a polyhedron that has triangular sides with a square base that meets up at a certain point, where a polyhedron means a three-dimensional figure with flat polygons as their sides. The different formula helps us to find the surface area, volume, or lateral edge length and height of the pyramid.

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Examples of Square Pyramid

  • The Pyramids of Egypt are the best examples of the Square Pyramid. The Pyramid of Khufu is not just the largest pyramid of Egypt but also one of the Seven Wonders of the Ancient World.

  • The Shape of a tent or sometimes the roofs of the buildings are designed in the form of Square-based Pyramids.

What are the Properties of the Square Pyramid?

From the meaning, it’s clear that it is something with a square-shaped base and four triangular sides that meets up at a certain point which reveals the following properties :

  • A Square Base

  • A top point where all sides meet called Apex

  • Four Triangular Faces

  • Five Vertices ( Four corner Points & One Top point )

  • Eight Edges

Types of Square Pyramids

There are two types of square pyramids which are discussed below:

Equilateral Square Pyramids: When the sides of the pyramid are equilateral triangles which means when the edges are equal then it is called an Equilateral Square Pyramid.


Right Square Pyramid: When all the lateral edges are of the same length and the sides except the base are congruent isosceles triangles, then it is called a Right Square Pyramid.


Volume of a Square Based Pyramid

General Square Pyramid Formula or Formula for Right Square Pyramid is mentioned below which can be used to calculate the volume:

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V = \[\frac{1}{3}\] × b2 × h

Or it can also be written as

V = \[\frac{1}{3}\] l2 h or \[\frac{1}{3}\]a2h

Here,

V = Volume of a square pyramid formula

l or a = base length

h = height of the pyramid


Examples

Some of the Examples of Calculation of Volume are Given Below:

  • The length of the base edge and height of the square pyramid is given as 5 and 9 units respectively. Calculate the volume of a square based pyramid.

V= \[\frac{1}{3}\]a2h

= \[\frac{1}{3}\] (5)2 9

= \[\frac{1}{3}\] × 25 × 9

= 75 cubic units

  •  John has a particular vessel that needs to be filled with liquid and this vessel is in the shape of an inverted regular square pyramid whose altitude is 12 inches whereas the base edge is 5 inches. Find out the volume of the vessel that can be filled with liquid?

V = \[\frac{1}{3}\] a2h

   =\[\frac{1}{3}\] × 5 2 × 12

   = \[\frac{1}{3}\] × 25 × 12

   = 100 cubic inches


Conclusion

Thus, to sum up, the discussion of the volume of a square pyramid formula, we can say that it is simply equal to the product of the length of the base and height of the pyramid with one third. If we know this formula, we can calculate the volume of the square pyramid easily. With the help of base length as well as height, volume can be calculated whereas if the volume of given and any one of the values either base length or height is missing, with the help of volume as well as other available elements, the required value can be obtained. Thus, in these cases as well this formula of volume of a square pyramid can be used.

FAQs (Frequently Asked Questions)

Question1. What Do You Mean by Square Pyramid?

Answer. It is a polyhedron that has triangular sides with a square base that meets at a certain point upwards, where polyhedron means a 3-D figure with flat polygons as their sides. It can be of two types and different formulas can be used to calculate different things such as volume, surface areas, etc.

Question2. What are the Types of Square Pyramids?

Answer. There are basically two types of the square pyramid which includes equilateral square pyramids in which the sides of the pyramid are equilateral triangles whereas the right square pyramid where all the lateral edges are of the same length whereas the sides except the base are congruent isosceles triangles.

Question3. How to Find the Volume of a Square Pyramid?

Answer. The volume of the square pyramid can be easily found with the help of a formula that is equal to the product of base length & height with one third. It can be represented in the following way:

V = 1/3a2h or V =13 × b2 × h, where ‘V’ is volume, ‘b’ or ‘a’ refers to base length and ‘h’ means height.

Question4. The Volume of the Square Pyramid Is Given as 96 cm3 and the Length of the Base of the Pyramid Is 6 cm. Calculate the Height.

Answer. The height of the square pyramid can be calculated with the following formula:

 V = 1/3a2h

96 =1/3 × 6 2 × h

96 = 12 × h

96/12= h

8 cm = h

Therefore, the height of the square pyramid is 8cm.