As you are aware, pyramids are one of the oldest structures constructed by the human. Ever wondered how much volume a pyramid takes up? Ever give a thought about how it is structured? Do you know how to find the volume of a square pyramid? This paper shall give you guidelines on how to find the volume of a square pyramid.
Definition and History of Pyramid
Pyramid in geometry are solid three dimensions with flat polygonal faces, straight edges and vertices. They are also known as polyhedron (Greek) connected to a polygonal base and a point, known as a vertex. Each of the base edge and vertex forms a triangle, called the lateral face which forms of a conical shape with a polygonal base.
A pyramid with n-sided base has
A well-structured pyramid has its vertex directly above the geometric center of its base. A regular pyramid having a regular polygonal base is usually referred to as a Right Pyramid whereas non-right pyramids are referred as oblique pyramids. When unspecified, a pyramid is generally considered as a Square Pyramid. A square pyramid is generally a pyramid having a square base and the vertex is perpendicular to the center of the square base. If all the faces of the pyramid are equal then it is said to be an equilateral square pyramid.
The geometry of pyramid all started from the ancient Egypt and Babylon, which later developed in ancient Greece. The volume of all the pyramids including the square pyramid was only known to the ancient Egyptians. Democritus was the first Greek mathematician who figured out how to find the volume of a square pyramid.
Types of Pyramids
Many types of pyramids are classified by their type of base. There are various types of pyramids listed below:
Square Pyramid and its Volume
In a square pyramid, the base of the pyramid is of square shape with triangular side faces. The vertex of the pyramid is intended to cast upon the center of the square base.
The volume of any pyramid can be calculated by the given expression
V= 1∕3 Bh
B is the area of square base and h is the height of the square pyramid.
Now, Let us consider the side of the square base is ‘b’ and the height of the square base is ‘h’, then the Area of the base will be B=b2 and the volume of a square pyramid will be given as
This formula can be used to determine the volume of all the sizes of the square pyramid.
b = b x b
b = 4 x 4 = 16 cm2
V =b x h
16 cm2 x 10 cm = 160 cm3
a2 + b2 = c2
By assigning the values which we have considered the equation would become
h2 + (b/2)2 = l2Where h is the perpendicular height of the right triangle, b/2 is the base length of the right triangle and l is the slant height of the right triangle.
b/2=5 cm l=10 cm
h2 + (b/2)2 = l2
h=√102 – 52
h=√100 – 25
8.66 cm is the perpendicular height of the pyramid from the center of the square base to the vertex of the pyramid. The value of h is needed to find out the volume of the square pyramid.
b= 10 cm h=8.66 cm
v = 1/3b2h
v = (1/3)*(10)28.66
v = 1/3 100 x 8.66
v = (1/3)*(866)
v = 288.66 cm3
The volume of the square pyramid is obtained using the slant height of the pyramid. This will really help you to find the volume of the square pyramid if you don’t know the height of the square pyramid. So the next time someone asks you, if you know how to find the volume of a square pyramid, you will know the answer, won’t you.