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
112,500 ft.3
112,500 feet cubed
337,500 ft.3
337,500 feet cubed
37,500 ft.3
37,500 feet cubed
98.33 ft.3
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 V = (1/3) * base area * height.
First, we need to calculate the base area. The top opening is 30 ft wide and 250 ft long, so the base area is 30 ft * 250 ft = 7500 ft^2.
Next, we need to calculate the height of the pyramid. The deepest part in the middle is 15 ft.
Now we can plug these values into the volume formula:
V = (1/3) * 7500 ft^2 * 15 ft.
Calculating this, we get:
V = (1/3) * 112500 ft^3.
So the capacity of the trench is 112,500 ft^3.
Therefore, the correct answer is:
112,500 ft.3