The image above is a square pyramid frustum.

To compute the volume of a square pyramid frustum, three essential parameters are needed and this 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}

V = ^{20(100 + (120) + 144)} ⁄ _{3}

V = ^{20(364)} ⁄ _{3}

V = ^{7280} ⁄ _{3}

V = 2426.6

Therefore, the** volume of the square pyramid frustum** is **2426.6 cm ^{3}.**

**Calculating the Height of a Square Pyramid Frustum when the Volume, Top Side Length and Base Side Length of the Square Pyramid Frustum is 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 cm^{3}, base side length is 14 cm and top side length is 18 cm.

This implies that;

V = Volume of the square pyramid frustum = 32 cm^{3}

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)}

h = ^{96} / _{(196 + 252 + 324)}

h = ^{96} / _{772}

h = 0.124

Therefore, the **height of the square pyramid frustum** is **0.124 cm.**

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.