The image above is a square pyramid frustum. To calculate the volume of a square pyramid frustum, three essential parameters are needed and these parameters are base side length (a), top side length (b), and height (h).
The formula for calculating the volume of a square pyramid frustum:
V = h(a² + ab + b²) ⁄ 3
Where;
V = Volume of a square pyramid frustum
a = Base side length of the square pyramid frustum
b = Top side length of the square pyramid frustum
h = Height of the square pyramid frustum
Let’s solve an example
Find the volume of a square pyramid frustum when the base side length is 10 cm with a top side length of 12 cm and a height of 20 cm.
This implies that;
a = Base side length of the square pyramid frustum = 10 cm
b = Top side length of the square pyramid frustum = 12 cm
h = Height of the square pyramid frustum = 20 cm
V = h(a² + ab + b²) ⁄ 3
V = 20(10² + (10 x 12) + 12²) ⁄ 3
Then, V = 20(100 + (120) + 144) ⁄ 3
V = 20(364) ⁄ 3
V = 7280 ⁄ 3
So, V = 2426.6
Therefore, the volume of the square pyramid frustum is 2426.6 cm3.
Calculating the Height of a Square Pyramid Frustum when the Volume, Top Side Length, and Base Side Length of the Square Pyramid Frustum are Given
h = 3V / (a2 + ab + b2)
Where;
h = Height of the square pyramid frustum
V = Volume of the square pyramid frustum
a = Base side length of the square pyramid frustum
b = Top side length of the square pyramid frustum
Let’s solve an example;
Find the height of a square pyramid frustum when the volume is 32 cm3, base side length is 14 cm and top side length is 18 cm.
This implies that;
V = Volume of the square pyramid frustum = 32 cm3
a = Base side length of the square pyramid frustum = 14 cm
b = Top side length of the square pyramid frustum = 18 cm
h = 3V / (a2 + ab + b2)
h = 32 x 3 / (142 + (14 x 18) + 182)
Then, h = 96 / (196 + 252 + 324)
h = 96 / 772
h = 0.124
Therefore, the height of the square pyramid frustum is 0.124 cm.
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How to Calculate the Volume of a Square Pyramid Frustum Using Nickzom Calculator
Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the volume of a square pyramid frustum.
To get the answer and workings of the volume of a square pyramid frustum 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 frustum 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 frustum according to the respective parameters which are the base side length (a), top side length (b), and height (h).
Now, enter the values appropriately and accordingly for the parameters as required by the example above where the base side length (a) is 10 cm, top side length (b) is 12 cm and height (h) is 20 cm.
Finally, Click on Calculate
As you can see from the screenshot above, Nickzom Calculator – The Calculator Encyclopedia solves for the volume of a square pyramid frustum and presents the formula, workings and steps too.
