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How To Find The Volume Of A Square Pyramid

How To Find The Volume Of A Square Pyramid
December 03, 2022

How To Find The Volume Of A Square Pyramid

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Want to Find the Volume of a Square Pyramid? Read On!

The volume of an object is described as three-dimensional space it takes up, but it's probably better to think of it as the volume of water, gas, or other substance it can hold. In any case, when presented with a square-based pyramid – such as the Egyptian pyramids – you can calculate its volume using a simple equation that needs the pyramid's height and one side's length along the foundation.

Let’s learn How to Find the Square Pyramid Volume?

What Is The Volume Of A Square Pyramid?

The volume contained between the five edges of a square pyramid is referred to as its volume. A volume of a square pyramid is one among the product of the base's area and the pyramid's altitude.

As a result,

volume = (1/3) (Base Area) (Height).

The quantity of unit cubes that can be into the square pyramid volume is measured in "cubic units." Mainly it is written as m3, cm3, in3, and so on.

Moreover, this pyramid is a five-sided 3D shape. A polyhedron (pentahedron) is basically based on four triangles and a square base that is attached to a vertex as shown. It has a square base and triangle side faces with a shared vertex. There are three parts to a square pyramid:

  • The summit of the pyramid is its highest point.
  • The foundation of the pyramid is the lowest square.
  • Faces refer to the pyramid's triangle sides.
  • The Great Pyramid of Giza, perfume bottles, and other square pyramids are examples.

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Source: CueMath

Volume of A Square Pyramid Formula

Here we will learn about the square pyramid. Here how we have solved the square pyramid volume can be easily found out if you know the base area and its height, here is the formula that should be considered:

The volume of a square pyramid = (1/3) Base Area × Height

What if we considered a usual type of square pyramid which includes equilateral triangles of sid ‘b’

Here is how we explained the formula:

The formula of a regular square pyramid volume = 1/3 × b2 × h

Where,

  • b is symbolised as the base of the square pyramid, and,
  • h represents the square pyramid height

Source: CueMath

All the pyramids are categorized based on their bases, such as:

  • Rectangular pyramid
  • Pentagonal pyramid
  • Hexagonal pyramid
  • Triangular pyramid
  • Square pyramid

Easiest Way to Calculate the Volume of a Square Pyramid…

The volume of a square pyramid is calculated using (1/3) Base Area Height, as we learnt in the previous section. Follow the steps below if you find the right way to calculate a square pyramid:

Step 1: Using the provided data, take note of the pyramid's dimensions, such as the base area and height.

Step 2: You need to multiply the area of the base by (1/3), then multiply by height.

Step 3: Use cubic units to get the final answer.

Then, we've studied the volume of a square pyramid, let's look at some solved cases to help us comprehend it better.

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Square Pyramid Properties

A square pyramid has the following characteristics:

  • It has five different faces.
  • Triangles make up the four side faces.
  • The foundation is square.
  • It has a total of five vertices (corner points)
  • It has eight edges.

Classes of Square Pyramid

Square pyramids can be classified into the following:

  • Right Square Pyramid
  • Equilateral Square Pyramid
  • Oblique Square Pyramid

Pyramid of the Equilateral Square

If most of the edges have the same length, the edges that are included in equilateral triangles, and the pyramid is a square pyramid.

A single edge-length parameter l will be used to classify the Johnson square pyramids. The h stands for height; A represents the surface area, and volume V in the pyramid looks like:

Right Square Pyramid

All of the lateral sides of right squares pyramids are generally the same in length, and its sides besides the bottom are equivalent isosceles triangles.

The equation for surface area and volume of a right square pyramid with a base length of l and a height of h is:

A Square Pyramid's Net

When we place the three-dimensional figure surface to horizontal, revealing each aspect of the figure, a net of a 3D shape is formed. Several nets can exist in a solid.

The square pyramid's net would level the vision, revealing all of the faces. When the net of the square pyramid is folded, the original 3d shape is revealed.

The following steps are followed to see if a net makes a solid:

  • The number of faces in both the solid and the net may be the same. In addition, the forms of the solid's faces must match the shapes of the network's equivalent faces.
  • Consider how the net will be folded to form the solid and whether all of the sides will fit together properly.
  • The square pyramid's nets come in handy when we need to locate them.

If you are stuck with the ways to find the Volume of a Square Pyramid then this guide may help you in clearing your doubts and solving the assignment queries!

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