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)

Question

Responses

98.33 ft.3
98.33 feet cubed

337,500 ft.3
337,500 feet cubed

37,500 ft.3
37,500 feet cubed

112,500 ft.3

Answer 1

To calculate the capacity of the trench, we need to find its volume.

The volume of an inverted rectangular pyramid is given by the formula:
Volume = (1/3) * base area * height

The base area is the product of the length and the width of the top opening, so base area = 30 ft * 250 ft = 7500 ft².

The height of the pyramid is the distance from the top opening to the deepest part, which is 15 ft.

Now we can substitute these values into the formula:
Volume = (1/3) * 7500 ft² * 15 ft
Volume = 125,000 ft³

Therefore, the capacity for this trench is 125,000 ft³.