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?
1. 37,500 ft.3
2. 112,500 ft.3
3. 337,500 ft.3
4. 98.33 ft.3
To find the capacity of the trench, we need to find 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 the area of the top opening of the trench, which is 30 ft * 250 ft = 7500 ft^2.
The height of the pyramid is the depth of the trench at its deepest part, which is 15 ft.
Therefore, the volume of the trench is:
Volume = (1/3) * 7500 ft^2 * 15 ft = 37,500 ft^3
Therefore, the capacity for this trench is 37,500 ft^3.
Hence, the answer is 1. 37,500 ft^3.