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)
• 112, 500 ft. 3
• 37, 500 ft. 3
337, 500 ft.3
•
98.33 ft.3
To find the capacity of the trench, we need to calculate the volume of the shape in ft^3.
First, we need to find the dimensions of the trench at its deepest part. Since the top opening is 30 ft wide and 250 ft long, the dimensions of the trench at its deepest part will be half of these dimensions, so 15 ft wide and 125 ft long.
Now, to calculate the volume of the upside-down rectangular pyramid, we use the formula V = (1/3) * base area * height. The base area of the trench at its deepest part is 15 ft * 125 ft = 1875 ft^2. The height is given as 15 ft.
Plugging these values into the formula, we get V = (1/3) * 1875 ft^2 * 15 ft = 9375 ft^3.
Therefore, the capacity of the trench is 9375 ft^3. None of the given answer choices match this, so there may be an error in the problem.