The volume of the frustum of a regular

triangular pyramid is 135 cu.m. The lower

base is an equilateral triangle with an edge

of 9 cm. The upper base is 8 m above the

lower base. What is the upper base edge in

meters?

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This answer was edited.The frustum of a solid is the portion of the solid that lies between one or two parallel planes cutting it.

Given that the lower base is an equilateral triangle with an edge of 9 m, thus, the area of the lower base is m.

Let the length of the upper base be , and the height of the cut-off pyramid be , then given that the upper base is 8 m above the lower base, i.e. .

Since the pyramid is regular, thus the bottom and top of the frustum are equilateral triangles (they are similar). This means that by the polygons similarity rules, the proportion of the heights of the cut-off pyramid and the entire pyramid is equal to the proportion of the lengths of the base edges.

Thus, , where is the length of the edge of the top base.

The area of the base of the cut-off pyramid (the top base of the frustum) is .

The volume of the frustum of a triangular pyramid is given by , where is the area of the lower base, is the area of the upper base, is the height of the original pyramid and is the height of the cut off upper pyramid.

Thus,

Multiplying through by the denominator, gives

.

.

.

.

Solving the quadratic equation gives that .

Substituting for into the equation for , gives that .

Therefore, the length of the top edge of the frustum is 3 m.