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?
a 37,500 ft.^3
b 337,500 ft.^3
c 112,500 ft.^3
d 98.33 ft.^3
To find the capacity of the trench, we can calculate the volume of the upside-down rectangular pyramid.
The formula for the volume of a rectangular pyramid is given by:
Volume = (1/3) * base area * height
In this case, the base area is given by the top opening, which is 30 ft * 250 ft = 7500 ft².
The height of the pyramid is the depth at the deepest part, which is 15 ft.
Plugging these values into the formula, we have:
Volume = (1/3) * 7500 ft² * 15 ft = 37500 ft³
So the capacity of the trench is 37,500 ft³.
Therefore, the correct answer is option a) 37,500 ft³.