Square Pyramid
A square pyramid is a three-dimensional geometrical shape with four lateral faces shaped as triangles, and a square base. The lateral faces are connected to the square base and meet at a common point called the apex of the pyramid.
A square pyramid has three main parts:
- Apex: The apex is the top point, or vertex of the pyramid.
- Base: A square shaped base forms a flat surface that can be used to place the pyramid on flat surfaces.
- Face: The triangle-shaped lateral faces are called faces.
The square pyramid has four lateral faces and one square base, as you can see in the image.
Volume of a Square Pyramid
The volume of a square pyramid is the quantity of space that is occupied by the square pyramid.
The formula for the volume (V) of the square pyramid is:
V = \(\frac{1}{3}\)Bh
In this formula, B is the area of the square base of the pyramid, and h is the height of the pyramid.
The unit of the volume of a square pyramid is expressed in cubic length units such as mm\(^3\), cm\(^3\), m\(^3\), km\(^3\), in\(^3\), ft\(^3\), yd\(^3\), mi\(^3\).
Solved Volume of Square Pyramid Examples
Example 1: Find the volume of a square pyramid with a base area of 40 square centimeters and a height of 18 centimeters.
Solution:
The base area is 40 cm\(^2\) and the height is 18 cm.
V = \(\frac{1}{3}\)Bh [Formula for the volume of a square pyramid]
= \(\frac{1}{3}\) x 40 x 18 [Substitute 40 for B and 18 for h]
= 240 cm\(^3\) [Simplify]
Hence, the volume of the square pyramid is 240 cubic centimeters.
Example 2: Calculate the side length of the base of a square pyramid having a volume of 64 cubic centimeters and a height of 12 centimeters.
Solution:
The volume is 64 cm\(^3\) and the height is 12 cm.
V = \(\frac{1}{3}\)Bh [Formula for the volume of a square pyramid]
64 = \(\frac{1}{3}\) x B x 12 [Substitute 64 for V and 12 for h]
64 = 4B [Divide]
B = \(\frac{64}{4}\) = 16 cm\(^2\) [Simplify]
The area of the base is 16 cm\(^2\).
B = s\(^2\) [Formula for the area of a square base]
16 = s\(^2\) [Substitute 16 for B]
s = 4 [Simplify]
Hence, the side length of the square base is 4 centimeters.
Example 3: John traveled to Egypt to see the pyramids there. His tour guide described the history of the pyramid and stated that it can hold 810,000 cubic feet of water and has a square base that is 90 feet long. Calculate the height of the pyramid according to the guide.
Solution:
Side length of square base, s = 90 ft
Area of base, B = s\(^2\) [Area of a square]
= 90\(^2\) [Substitute 90 for s]
= 8100 ft\(^2\)
Apply the formula for the volume of a square pyramid.
V = \(\frac{1}{3}\)Bh
810000 = \(\frac{1}{3}\) x 8100 x h [Substitute 810000 for V and 8100 for B]
810000 = 2700h [Multiply]
h = \(\frac{810000}{2700}\) [Simplify]
= 300
So, the height of the pyramid is 300 feet.
The three main parts of a square pyramid are the apex, the square base, and the faces.
A square pyramid is a three-dimensional geometrical shape with four triangular lateral faces and a square base.
The volume of a square pyramid is the amount of space that has been occupied by the square pyramid.
Cubic units are used to measure the volume of a square pyramid. For example, cubic meters, cubic centimeters, liters (l) and many more.
A square pyramid has eight edges.