Volume of a pyramid

Look carefully at the pyramid shown below. The volume of a pyramid can be computed as shown

We will start with a pyramid that has a square as the base.

Pyramid:

Volume = (B × h)/3

B is the area of the base
h is the height

The base of the pyramid can be a rectangle, a triangle, or a square. Compute the area of the base accordingly

Volume of a square pyramid

Example #1:

A square pyramid has a height of 9 meters. If a side of the base measures 4 meters, what is the volume of the pyramid?

Since the base is a square, area of the base = 4 × 4 = 16 m²

Volume of the pyramid = (B × h)/3 = (16 × 9)/3 = 144/3 = 48 m³

Volume of a rectangular pyramid

Example #2:

A rectangular pyramid has a height of 10 meters. If the sides of the base measure 3 meters and 5 meters, what is the volume of the pyramid?

Since the base is a rectangle, area of the base = 3 × 5 = 15 m²

Volume of the pyramid = (B × h)/3 = (15 × 10)/3 = 150/3 = 50 m³

Volume of a triangular pyramid

Example: #3

A triangular pyramid has a height of 8 meters. If the triangle has a base of 4 meters and a height of 3 meters, what is the volume of the pyramid?

Notice that here, you are dealing with two different heights. Avoid mixing the height of the pyramid with the height of the triangle

Since the base is a triangle, area of the base = (b × h)/2 = (4 × 3)/2 = 12/2 = 6 m²

Volume of the pyramid = (B × h)/3 = (6 × 8)/3 = 48/3 = 16 m³