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:

Pyramid with height h
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



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



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



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

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