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The volume of a pyramid is just the space described between the faces of pyramid and it equals one-third multiplied by the product of the base area and height. If we consider a square pyramid, we understand that the pyramid's base is square, hence the volume formula changes accordingly. In this following article, we discuss and understand about the volume of Square pyramids in detail.
Read Also: Difference between area and volume
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What is Square Pyramid ?
A square pyramid is a polyhedron with triangular sides and a square base that intersect at a particular point, where a polyhedron is defined as a three-dimensional shape having flat polygons as its sides. In simple terms, a square pyramid is a kind of pyramid who has a square-shaped base and 4 triangular faces which connect each other at a particular point known as vertex.
Pyramid
Some Examples of Square Pyramid
- The best examples of the Square Pyramid are the Egyptian Pyramids. The Pyramid of Khufu is Egypt's greatest pyramid, and also one of the Seven Wonders.
- Triangular shaped tent are also one of the prominent examples of square-based pyramids.
Square based Pyramid
Properties of the Square Pyramid
It's evident from the definition that it's something with a square base and four triangular sides that meet at a point and reveal the following characteristics:
- A square base
- Apex is a top point where all sides meet.
- There are four triangular faces.
- There are five vertices ( Four corner Points & One Top point )
- Eight Corners
Read also: Volume and areas
Types of Square Pyramids
There are two types of square pyramids given below :
Equilateral Square Pyramids:
An Equilateral Square Pyramid is defined by the sides of the pyramid being equilateral triangles, which means the edges are equal.
Right Square Pyramid:
A Right Square Pyramid is formed when all of the lateral edges are of similar length and all of the sides except the base are congruent isosceles triangles.
Volume of a Square Based Pyramid
General Square Pyramid Formula or Formula for Right Square Pyramid is given below which can be used to determine the volume:
V =1/3×b2 ×h
Or it can also be stated as,
V= 1/3 l2h Or 1/2a2h
Here,
V refers to a Volume of a square pyramid formula
l or a is stated as base length
H is the height of the pyramid
Volume of Square Pyramid
Square Pyramid Net
A net diagram shows each face and base with all of its dimensions, resulting in a flattened picture of any solid shape.
Pyramid net of square-based pyramid is made up of 2D faces that can be folded to form a 3D shape. It's similar to unfolding a pyramid and flattening it totally. The graphic below depicts how it might appear.
Square Pyarmid Net
To make a pyramid, fold the four sides together here. A pyramid net allows you to clearly view every face of the pyramid.
In mathematics, a square pyramid net is useful for teaching 3D shapes.
How to Draw a Square Pyramid?
Pyramids are tough to sketch on paper because they are three-dimensional structures. It necessitates angle precision so that it appears as a three-dimensional shape on paper. We'll take a step-by-step look at how to draw a square pyramid. Let's look at what we'll need to make the pyramid:
Step 1 – First decide the size of the pyramid you want to create; in this case, a square with a side of 5 cm would suffice.
Step 2: At the base of the pyramid, create a 5 cm line. Measure 5 cm from the tip of your compass to the pencil.
Step 3 – With the help of your compass, draw a circle at one end of the baseline. Rep on the opposite side of the baseline. Both lines should cross in the middle if everything is done correctly.
Step 4 – Now join the two ends of the triangle from the baseline to the top.
Step 5: Rub out the lines you drew in the previous step.
Step 6 – Draw an extension to one side of the triangle, making sure the baseline of that side is higher than the original baseline you made.
As a result, your square pyramid on paper is complete.
Square Pyramid
Points to remember
- The volume of a pyramid is just the space described between the faces of pyramid and it equals one-third multiplied by the product of the base area and height.
- A square pyramid is a kind of pyramid who has a square-shaped base and 4 triangular faces which connect each other at a particular point known as vertex.
- The formula to calculate the volume of square based pyramid is V =1/3×b2 ×h
- There are two types of Square Pyramids, Equilateral Square Pyramids and Right Square Pyramid.
Also read:
FAQs (Frequently asked questions) :
Ques. Julia needs to fill a vessel in the shape of an inverted regular right square pyramid with water. The vessel’s height is given 10 inches, and the base edge’s length is given 7 inches. Now calculate and determine the volume of water Julia can fill the vessel with?
Solution: Given info,
h = 10 inches and ,
b = 7 inches
The volume of the vessel is stated as V = 1/3 × b2 × h
⇒ V = 1/3 × 72 × 10
⇒ V = 490/3
⇒ V = 163.33 cubic inches
Hence, the volume of the vessel is 163.33 in3.
Ques. Calculate the volume of a square pyramid of base length 6 cm and height 8 cm.
Solution:
Given,
A = 6 cm
H = 8 cm
Volume of a square pyramid
= 1/3 A2h
= 1/3 × (6 cm)2 × 8 cm
= 1/3 × 36 cm2 × 8 cm
= 96 cm3
Ques. Determine the volume of a square-base pyramid with the given information : The base has 12 cm on each side and a height of 21 cm.
Solution.
We Determine the volume of a pyramid with the help of formula = V = ? A H
Since the base of the pyramid is a square, the area of the base is a2 = 12 x 12 = 144 cm2
= ? x 144 cm2 x 21 cm
= 144 x 7
= 1008 cm3
Ques. Calculate the volume of a square-base pyramid? The base's sides are 10 cm apiece, and the pyramid's height is 18 cm.
Solution.
We determine the volume of a pyramid by using the formula = V = ? A H
Since the base of the pyramid is a square, the area of the base is a2 = 10 x 10 = 100 cm2
= ? x 100 cm2 x 18 cm
= 100 x 6
= 600 cm3
Ques. A square pyramid has a base length of 13 cm and a height of 20 cm. Determine the volume of the pyramid.
Solution.
Given,
Length of the base, a = 13 cm
height = 20 cm
Volume of a square pyramid = 1/3 a2 h
By substitution, we get,
Volume = 1/3 x 13 x 13 x 20
= 1126.7 cm3
Ques. Given the volume of a square pyramid is 625 cubic feet. So If the height of the pyramid is stated 10 feet, then Calculate are the dimensions of the pyramid’s base?
Solution. Given,
Volume = 625 cubic feet.
height = 10 feet
With the help of formula of volume of a square,
⇒ 625 = 1/3 a2 h
⇒ 625 = 1/3 x a2 x 10
⇒ 625 = 3.3a2
⇒ a2 =187.5
⇒ a = = √187.5
a =13.7 feet
Hence, the dimensions of the base will be 13.7 feet by 13.7 feet.
Ques. The length of a base of a square pyramid is given twice the height of the pyramid, Now Determine and calculate the dimensions of the pyramid if it has a volume of 48 cubic yards.
Solution.
Let's take the height of the pyramid as x
the length = 3x
volume = 48 cubic yards
But, the volume of a square pyramid = 1/3 a2 h
Substitute.
⇒ 48 = 1/3 (3x)2 (x)
⇒ 48 = 1/3 (9x3)
⇒ 48 = 3x3
Divide both sides by 3 to get,
⇒ x3 =16
⇒ x = 3√16
x = 2.52
Hence, the height of the pyramid = x ⇒2.53 yards, and each side of the base is 7.56 yards
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