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Volume of a Pyramid

A pyramid is a polyhedron with one base that is any polygon . Its other faces are triangles.

Math diagram

The volume of a 3 -dimensional solid is the amount of space it occupies.  Volume is measured in cubic units ( in 3 , ft 3 , cm 3 , m 3 , et cetera).  Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a pyramid is one-third the area of the base B times the height h .

V = 1 3 B h


Find the volume of a regular square pyramid with base sides 10 cm and altitude 18 cm.


Draw a figure.

Math diagram

The formula for the volume of a pyramid is,

V = 1 3 B h

Since the base of the pyramid is a square, the base area is 10 2 or 100 cm 2 .

So, substitute 100 for B and 18 for h in the formula.

V = 1 3 ( 100 ) ( 18 ) = 600

Therefore, the volume of the square pyramid is 600 cm 3 .


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