Introduction:
In geometry, we have two-dimensional shape and three dimensional shape. Pyramid is a thee dimensional shape. It is also called as Polyhedron. The base of pyramid may be square, rectangle, triangle or any other polygon shape. The sides of pyramid look triangular faces. In Pyramid, all vertices of base are connecting a point to above, it is called apex of pyramid.
We have various kind of three dimensional pyramids. They are following.
For example, we have Square based pyramid, Rectangular pyramid, Triangular Pyramid, Pentagonal pyramid, Hexagonal pyramid and etc.
In this article, we will see about volume of all kinds of three dimensional pyramid.
Three Dimensional Pyramid: Square Pyramid, Rectangle Pyramid
Square based pyramid:
It is a three dimensional pyramid shape having a base is square. In square pyramid, we have five vertices, four triangular faces.
Formula:
Volume of square pyramid = `1/3*base^2*height`
Example 1:
Find the volume of square pyramid for the given base side is 7 meter and height is 10 meter.
Solution:
Given:
Base side = 7 m
Height = 10 m
Volume of square pyramid = `1/3*base^2*height`
= `1/3*7^2*10`
= 0.333 * 49 * 10
= 163.17
Therefore, Volume of square pyramid is 163.2 cubic meter.
Rectangular pyramid:
It is a three dimensional pyramid shape having a base is Rectangle. In Rectangle pyramid, we have five vertices, four triangular faces.
Formula:
Volume of Rectangular pyramid = `1/3*LenGth*width*height`
Example 2:
Find the volume of Rectangular pyramid for the given length is 10 meter , width is 8 meter and height is 12 meter.
Solution:
Given:
Length = 10 m
Width = 8 m
Height = 12 m
Volume of rectangular pyramid = `1/3*LenGth*width*height`
= `1/3*10*8*12`
= 0.333 * 960
= 319.68
Therefore, Volume of Rectangular pyramid is 319.7 cubic meter.
Three Dimensional Pyramid: Triangular Pyramid, Hexagonal Pyramid
Triangular pyramid:
It is a three dimensional pyramid shape having a base is Triangle. In triangular pyramid, we have four vertices, four triangle faces.
Formula:
Volume of triangular pyramid = `1/6*base*height*HEIGHT`
Example 3:
Find the volume of triangular pyramid for the given base is 6 meter , height is 10 meter and HEIGHT is 12 meter.
Solution:
Given:
Base = 6 m
Height = 10 m
HEIGHT = 12 m
Volume of Triangular pyramid = `1/6*base*height*HEIGHT`
= `1/6*6*10*12`
= 0.167 * 720
= 120.24
Therefore, Volume of triangular pyramid is 120.2 cubic meter.
Hexagonal pyramid:
It is a three dimensional pyramid shape having a base is Hexagon. In Hexagonal pyramid, we have seven vertices, six triangle faces.
Formula:
Volume of Hexagonal pyramid = `Apothem*Side*Height`
Example 3:
Find the volume of Hexagonal pyramid for the given side is 6 meter , height is 10 meter and Apothem is 7 meter.
Solution:
Given:
Side = 6 m
Height = 10 m
Apothem = 7 m
Volume of Hexagonal pyramid = `Apothem*Side*Height`
= `7*6*10`
= 420
Therefore, Volume of Hexagonal pyramid is 420 cubic meter.
In geometry, we have two-dimensional shape and three dimensional shape. Pyramid is a thee dimensional shape. It is also called as Polyhedron. The base of pyramid may be square, rectangle, triangle or any other polygon shape. The sides of pyramid look triangular faces. In Pyramid, all vertices of base are connecting a point to above, it is called apex of pyramid.
We have various kind of three dimensional pyramids. They are following.
For example, we have Square based pyramid, Rectangular pyramid, Triangular Pyramid, Pentagonal pyramid, Hexagonal pyramid and etc.
In this article, we will see about volume of all kinds of three dimensional pyramid.
Three Dimensional Pyramid: Square Pyramid, Rectangle Pyramid
Square based pyramid:
It is a three dimensional pyramid shape having a base is square. In square pyramid, we have five vertices, four triangular faces.
Formula:
Volume of square pyramid = `1/3*base^2*height`
Example 1:
Find the volume of square pyramid for the given base side is 7 meter and height is 10 meter.
Solution:
Given:
Base side = 7 m
Height = 10 m
Volume of square pyramid = `1/3*base^2*height`
= `1/3*7^2*10`
= 0.333 * 49 * 10
= 163.17
Therefore, Volume of square pyramid is 163.2 cubic meter.
Rectangular pyramid:
Formula:
Volume of Rectangular pyramid = `1/3*LenGth*width*height`
Example 2:
Find the volume of Rectangular pyramid for the given length is 10 meter , width is 8 meter and height is 12 meter.
Solution:
Given:
Length = 10 m
Width = 8 m
Height = 12 m
Volume of rectangular pyramid = `1/3*LenGth*width*height`
= `1/3*10*8*12`
= 0.333 * 960
= 319.68
Therefore, Volume of Rectangular pyramid is 319.7 cubic meter.
Three Dimensional Pyramid: Triangular Pyramid, Hexagonal Pyramid
Triangular pyramid:
Formula:
Volume of triangular pyramid = `1/6*base*height*HEIGHT`
Example 3:
Find the volume of triangular pyramid for the given base is 6 meter , height is 10 meter and HEIGHT is 12 meter.
Solution:
Given:
Base = 6 m
Height = 10 m
HEIGHT = 12 m
Volume of Triangular pyramid = `1/6*base*height*HEIGHT`
= `1/6*6*10*12`
= 0.167 * 720
= 120.24
Therefore, Volume of triangular pyramid is 120.2 cubic meter.
Hexagonal pyramid:
It is a three dimensional pyramid shape having a base is Hexagon. In Hexagonal pyramid, we have seven vertices, six triangle faces.
Formula:
Volume of Hexagonal pyramid = `Apothem*Side*Height`
Example 3:
Find the volume of Hexagonal pyramid for the given side is 6 meter , height is 10 meter and Apothem is 7 meter.
Solution:
Given:
Side = 6 m
Height = 10 m
Apothem = 7 m
Volume of Hexagonal pyramid = `Apothem*Side*Height`
= `7*6*10`
= 420
Therefore, Volume of Hexagonal pyramid is 420 cubic meter.
