The height and side of the base of a regular quadrangular pyramid is 4. Find the volume of the pyramid.

The volume of a regular pyramid is calculated as 1/3 of the product of the area of its base by the height.

V = 1/3 ∙ Sb. ∙ h.

Height h = 4 m by condition, at the base of the regular pyramid there is a regular polygon. In this case, a regular quadrangular pyramid is given. This means that a regular quadrangle – a square – lies at the base. Let’s find its area.

Sosn. = Sq. = a ^ 2 = 4 ^ 2 = 16 m2.

Let’s find out what the volume of the pyramid is.

V = 1/3 ∙ 16 ∙ 4 = 1/3 ∙ 64 = 211/3 m3.

Answer: V = 211/3 m3.