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

337,500 ft.3
337,500 feet cubed

112,500 ft.3
112,500 feet cubed

37,500 ft.3
37,500 feet cubed

98.33 ft.3
98.33 feet cubed

Answer 1

To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.
The formula for the volume of a rectangular pyramid is given by:
Volume = (1/3) * base area * height.

First, let's calculate the base area:
The top opening of the trench is 30 ft. wide by 250 ft. long. So the base area is:
Base area = 30 ft * 250 ft = 7500 ft².

Now, let's calculate the height:
The deepest part in the middle is given as 15 ft.

Using the formula for volume, we have:
Volume = (1/3) * 7500 ft² * 15 ft = (1/3) * 112,500 ft³ = 37,500 ft³.

Therefore, the capacity of the trench is 37,500 ft.³