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 drainage trench, we first need to find the volume of the upside-down rectangular pyramid.
The volume of a pyramid is given by the formula:
V = (1/3) * base area * height
First, let's find the dimensions of the base of the pyramid. Since the top opening is a rectangle with dimensions 30 ft. by 250 ft., the base of the pyramid will also be a rectangle with the same dimensions.
Given:
Base length (l) = 250 ft
Base width (w) = 30 ft
Height (h) = 15 ft
Now, we can calculate the base area:
Base area = l * w
Base area = 250 ft * 30 ft
Base area = 7500 sq. ft
Now, we can calculate the volume of the pyramid:
V = (1/3) * base area * height
V = (1/3) * 7500 sq. ft * 15 ft
V = 3750 cubic ft
Therefore, the capacity of the drainage trench is 3750 cubic ft.