Originally Posted by

**ticbol** I'd call it a truncated inverted right triangular pyramid.

It is the top part of an inverted large vertical right triangular pyramid that is cut horizontally at 58 ft from the top.

The large pyramid has a total vertical height of (y +58) ft.

To solve for the y, draw an inverted triangle whose top is 7 ft wide.

Then 58 ft below the top is 6 ft wide.

The bottom is zero ft wide, of course.

By proportion,

(y +58)/7 = y/6

Cross multiply,

6(y +58) = 7y

6y +348 = 7y

348 = 7y -6y

y = 348 ft

So, the total height of the large pyramid is 348 +58 = 406 ft.

volume of pyramid is (1/3)(area of base)(altitude)

The volume, V, of the large pyramid is

V = (1/3)(24.5)(406) = 3315.67 cu.ft.

The volume, V1, of the cut pyramid is

V1 = (1/3)(18)(348) = 2088 cu.ft.

Therefore, the volume of that truncated thing is

3315.67 -2088 = 1227.67 cu.ft. -------answer.