Volume of Pyramid

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A pyramid is a 3-dimensional geometric figure consisting of a base and triangles placed on the particular base of the pyramid. The line joining the center of the base to the vertex of the pyramid (the top-most point is known as the ‘apex’ or the ‘vertex’) is called the height of the pyramid. Volume of a pyramid gives us the amount of space contained inside the given pyramid and volume of any pyramid is one-third times the product of the area of the base and the height of the pyramid.

 Example 1: Calculate the volume of a square pyramid whose base length is 5.5m and the height is 12m?

Given base length of the pyramid, b = 5.5m

Height of the pyramid, h = 12m

Volume of the pyramid, V = 1/3 * Area of the base * height

 Area of the square base = b2 = (5.5m)2 = 30.25m2   

Volume of the square pyramid, V = 1/3 * 30.25m 2 * 12m = 121m3

Therefore, volume of the given square pyramid, V = 121m3

 Example 2:Calculate the volume of a triangular pyramid whose triangular base length is 3.5m, height of the base triangle is 6m and the height of the pyramid is 10m.

Given base length of the pyramid, b= 3.5m

Height of the base triangle, h= 6m

Height of the pyramid, H= 10m

Volume of the pyramid, V= 1/3* Area of the base* Height of pyramid

Area of the triangular base= 1/2* b* h = 1/2* 3.5m* 6m= 10.5m2

Volume of the triangular pyramid, V= 1/3* 10.5m 2 * 10m= 35m3

Therefore, volume of the given triangular pyramid, V= 35m3

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