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 trench, we need to calculate the volume of the pyramid shape.
The volume of a pyramid is given by the formula V = 1/3 * base area * height.
First, we need to calculate the base area of the pyramid. Since the top opening is a rectangle with dimensions 30 ft. by 250 ft., the base area is 30 ft. * 250 ft. = 7500 sq. ft.
Next, we need to find the height of the pyramid. The height is the depth of the trench in the middle, which is 15 ft.
Now, we can calculate the volume of the pyramid:
V = 1/3 * 7500 sq. ft. * 15 ft.
V = 1/3 * 112500 cu. ft.
V = 37500 cu. ft.
Therefore, the capacity of the drainage trench is 37500 cubic feet.