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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 98.33 ft.3 98.33 feet cubed 37,500 ft.3

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To find the capacity of the upside-down rectangular pyramid-shaped trench, we can use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

  1. Calculate the Base Area: The base of the pyramid is rectangular, with dimensions:

    • Width = 30 ft
    • Length = 250 ft

    So, the base area is: \[ \text{Base Area} = 30 , \text{ft} \times 250 , \text{ft} = 7,500 , \text{ft}^2 \]

  2. Determine the Height: The height of the pyramid (the deepest part of the trench) is given as 15 ft.

  3. Calculate the Volume: Now plug the values into the volume formula: \[ V = \frac{1}{3} \times 7,500 , \text{ft}^2 \times 15 , \text{ft} \] \[ V = \frac{1}{3} \times 112,500 , \text{ft}^3 \] \[ V = 37,500 , \text{ft}^3 \]

Thus, the capacity of the trench is 37,500 ft³.