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 point)
Responses
To calculate the capacity of the trench, we need to find the volume of the upside-down rectangular pyramid.
The formula for the volume of a pyramid is V = 1/3 * base area * height.
First, we need to find the area of the top opening of the pyramid:
Area = length * width = 30 ft. * 250 ft. = 7500 sq. ft.
Next, we need to find the average base length (b) of the pyramid, which is the average of the top and bottom lengths.
b = (30 ft. + 0 ft.) / 2 = 15 ft.
Now, we can calculate the volume of the pyramid:
V = 1/3 * 7500 sq. ft. * 15 ft.
V = 1/3 * 112,500 cu. ft.
V = 37,500 cu. ft.
Therefore, the capacity of the drainage trench is 37,500 cubic feet.