The image above represents a square pyramid.

To compute 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}

V = ^{11(36)} / _{3}

V = ^{396} / _{3}

V = 132

Therefore, the **volume of the square pyramid** is **132 cm**^{3}.

**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 cm^{3} and a height of 20 cm.

This implies that;

V = Volume of the square pyramid = 50 cm^{3}

h = height of the square pyramid = 20 cm

a = √(^{3V} / _{h)}

a = √(^{3(50)} / _{20)}

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 cm^{3} and a base edge of 7 cm^{2}

This implies that;

V = Volume of the square pyramid = 250 cm^{3}

a = Base edge of the square pyramid = 7 cm

h = ^{3V} / _{a²}

h = ^{3(250)} / _{7²}

h = ^{750} / _{49}

h = 15.306

Therefore, the** height of the square pyramid **is** 15.306 cm.**

Continue reading How to Calculate and Solve for the Height, Base Edge and Volume of a Square Pyramid | The Calculator Encyclopedia