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. 98.33 ft.^3
b. 37,500 ft.^3
c. 112,500 ft.^3
d. 337,500 ft.^3
To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.
The formula to calculate the volume of a rectangular pyramid is:
Volume = (1/3) * base area * height
The base area of the pyramid is the area of the top opening, which is 30 ft. wide by 250 ft. long, so:
Base area = 30 ft. * 250 ft. = 7500 ft.^2
The height of the pyramid is the depth of the trench in the middle, which is 15 ft.
Now let's substitute the values into the formula:
Volume = (1/3) * 7500 ft.^2 * 15 ft.
Volume = 37500 ft.^3
Therefore, the capacity for this trench is 37,500 ft.^3
So, the correct answer is: b. 37,500 ft.^3