A construction company is digging a drainage trench. It makes the shape of an upside-down rectangular pyramid. The top opening will be 30 ft. wide by 250 ft. long, and the deepest part in the middle will be 15 ft. What is the capacity for this trench
To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.
The formula for the volume of a rectangular pyramid is:
Volume = (1/3) * base area * height
In this case, the base area is the area of the top opening, which is 30 ft. wide by 250 ft. long:
Base area = 30 ft * 250 ft = 7500 ft²
The height of the pyramid is the deepest part in the middle, which is 15 ft.
Now we can calculate the volume:
Volume = (1/3) * 7500 ft² * 15 ft
= 1/3 * 112,500 ft³
= 37,500 ft³
So, the capacity of the drainage trench is 37,500 cubic feet.