How much water does a pit dug in the form of a truncated pyramid hold, if the depth of the pit is 1.5 m, the side

How much water does a pit dug in the form of a truncated pyramid hold, if the depth of the pit is 1.5 m, the side of the lower square base is 0.8 m, and the upper one is 1.2 m.

Imagine the pit as an inverted truncated pyramid.

Since there are squares in the bases, we determine the areas of both bases.

S1 = AB * AD = 1.2 * 1.2 = 1.44 m2.

S2 = A1B1 * A1D1 = 0.8 * 0.8 = 0.64 m2.

The depth of the pit is the height of the truncated pyramid.

Let’s define the volume of the truncated pyramid.

V = OO1 * (S1 + S2 * √S1 * S2) / 3 = 1.5 * (1.44 + 0.64 * √1.44 * 0.64) / 3 = 1.5 * 3.04 / 3 = 1.52 m3.

Answer: The volume of the pit is 1.52 m3.