How to Calculate and Solve for the Height, Base Edge and Volume of a Square Pyramid | The Calculator Encyclopedia
Last Updated on February 16, 2024
The image above represents a square pyramid. To calculate the volume of a square pyramid requires two essential parameters which are the base edge and height of the square pyramid.
The formula for computing the volume of a square pyramid is:
V = ha² / 3
Where:
V = Volume of the Square Pyramid
a = Base edge of the Square Pyramid
h = Height of the Square Pyramid
Let’s solve an example
Find the volume of a square pyramid with a base edge of 6 cm and a height of 11 cm.
This implies that:
a = base edge of the square pyramid = 6
h= = height of the square pyramid = 11
V = ha² / 3
V = 11(6)² / 3
So, V = 11(36) / 3
V = 396 / 3
V = 132
Therefore, the volume of the square pyramid is 132 cm3.
Calculating the Base edge of a square pyramid when Volume and Height are Given
The formula is a = √(3V / h)
Where;
V = Volume of the Square Pyramid
a = Base edge of the Square Pyramid
h = Height of the Square Pyramid
Let’s solve an example:
Find the base edge of a square pyramid with a volume of 50 cm3 and a height of 20 cm.
This implies that;
V = Volume of the square pyramid = 50 cm3
h = height of the square pyramid = 20 cm
a = √(3V / h)
a = √(3(50) / 20)
That is, a = √(150 / 20)
a = √7.5
a = 2.739
Therefore, the base edge of the square pyramid is 2.739 cm.
Calculating the height of a square pyramid when Volume and Base edge are Given
The formula is h = 3V / a2
Where;
a = Base edge of the square pyramid
V = Volume of the Square Pyramid
h = Height of the Square Pyramid
Let’s solve an example:
Find the height of a square pyramid with a volume of 250 cm3 and a base edge of 7 cm2
This implies that;
V = Volume of the square pyramid = 250 cm3
a = Base edge of the square pyramid = 7 cm
h = 3V / a²
h = 3(250) / 7²
Then, h = 750 / 49
h = 15.306
Therefore, the height of the square pyramid is 15.306 cm.
How to Calculate and Solve for the Volume of a Square Pyramid Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the volume of a square pyramid.
To get the answer and workings of the volume of a square pyramid using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.
You can get this app via any of these means:
Web – https://www.nickzom.org/calculator-plus
To get access to the professional version via web, you need to register and subscribe for NGN 1,500 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator
Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Mensuration under the Mathematics section.
Now, click on Volume of a Square Pyramid under Mensuration
The screenshot below displays the page or activity to enter your values, to get the answer for the volume of a square pyramid according to the respective parameters which are the base edge and height of the square pyramid.
Now, enter the values appropriately and accordingly for the parameters as required by the example above where the base edge of the square pyramid is 6 cm and the height of the square pyramid is 11 cm.
Finally, click on the Calculate button
As you can see from the screenshot above, Nickzom Calculator – The Calculator Encyclopedia solves for the volume of a square pyramid and presents the formula, workings and steps too.
