Volume of a Pyramid Formula

Volume of a Square Based Pyramid

If we connect a polygon base with a random point, a geometrical polyhedron will be formed. It is known as a pyramid. The total space occupied by any three-dimensional solid or pyramid is said to be the volume of a pyramid. Generally, cubic units are used to measure volume. Hence, units of all the computational terms need to be equal before computing the volume. The volume of a pyramid formula is one-third times the height of the pyramid multiplied by the base area. Here, we will learn to compute the volume of a square pyramid.


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Volume Formula for Different Types of Pyramid

Below we have the formula for the volume of different types of pyramids which has been derived from the basic formula itself.

  • Volume of a Rectangular Pyramid:

(1/3) × (height) × (length of the base) × (width of base)

  • Volume of a Triangular Pyramid:

(1/6) × (pyramid’s apothem length) × (length of pyramid’s base) × (height)

  • Volume of a Square Pyramid:

(1/3) × (height) × (length of pyramid’s base) × (length of pyramid’s base) or (1/3) × (height) × (length of pyramid’s base)2

  • The Volume of a Hexagonal Shaped Pyramid:

(pyramid’s apothem length) × (length of pyramid’s base) × (height)

  • The Volume of Pentagonal Shaped Pyramid:

(5/6) × (pyramid’s apothem length) × (length of pyramid’s base) × (height)


Conclusion

With proper conceptual understanding, the volume of a pyramid formula can be easily calculated. Besides on a lighter note, from now onwards if you are planning to visit Egypt, you know how exactly one can calculate the volume of a pyramid. All you need to do is measure some parameters.

FAQs (Frequently Asked Questions)

Q1. What is a Pyramid? Explain Relevant Terms Related to it.

Answer: As already stated, any point connected to a polygonal base forms a pyramid. The random point to which we connect the base is called the apex of the pyramid. Every pyramid has a lateral face which is formed by connecting one of the base edges with the apex point. The lateral face is a triangular side of the pyramid. Hence, for a pyramid, only the base can be any polygon while the other sides are triangular. There are various types of pyramids such as square, triangular, rectangular, pentagonal, hexagonal, and more depending on the base. Now let’s look at how to compute the volume of a rectangular pyramid and triangular pyramid volume formula.

Q2. What is the Simplest Way to Calculate the Volume of any Pyramid Supposedly with a Height of 3 Units and a Square Base of Sides 2 Units?

Answer: The first step to finding the volume of any pyramid is to find the area of the base. Once, you have successfully calculated the base area, the next step is to find the height of the pyramid. With the help of the base measurements and slant height of the pyramid, you can easily get the height. Next, you multiply the base area with the height and divide it by three. And there you have the volume of the pyramid.


And in this case with the values given,

The volume of pyramid= 1/3 × (base length)2 × height

                                    = 1/3 × (2)2 × 3 = 4 cubic units.

Q3. How to Calculate the Volume of a Rectangular Pyramid?

Answer: With proper concepts, one can easily calculate the volume of difficult three dimensional shapes. Pyramids are one of the most widely found volumes. Now, rectangular pyramids have a rectangular or four sided base with four sides that are triangular. All of these come together and join at a random point known as the apex. The first step is to find the area of the base by multiplying the length and breadth of the base. Next, you find out the height which is the distance between the apex and the centre of the base and multiply it with the base area. Finally one needs to divide the result by three to get the final volume of a rectangular pyramid.