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
98.33 ft.^3
37,500 ft.^3
112,500 ft.^3
337,500 ft.^3
To find the capacity of the trench, we first need to find 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
The base area is equal to the product of the length and width of the top opening of the trench, which is 30 ft * 250 ft = 7500 ft^2.
The height of the trench is the difference between the deepest part and the top opening, so it is 15 ft.
Substituting these values into the formula, we get:
Volume = (1/3) * 7500 ft^2 * 15 ft = 37,500 ft^3
Therefore, the capacity for this trench is 37,500 ft^3. Hence, the correct answer is B) 37,500 ft^3.