Volume of Pyramid
Look carefully at the pyramid shown below. The volume of a pyramid can be computed as shown:
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.
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.
----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 square meters
Volume of the pyramid = (B × h)/3 = (16 × 9)/3 = 144/3 = 48 cubic meters
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 square meters
Volume of the pyramid = (B × h)/3 = (16 × 9)/3 = 144/3 = 48 cubic meters
----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 square meters
Volume of the pyramid = (B × h)/3 = (15 × 10)/3 = 150/3 = 50 cubic meters
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 square meters
Volume of the pyramid = (B × h)/3 = (15 × 10)/3 = 150/3 = 50 cubic meters
----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
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