To find the capacity of the drainage trench in the shape of an upside-down rectangular pyramid, we can use the formula for the volume of a pyramid:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
In this case, the base area is the area of the top opening of the trench, which is a rectangle:
- Width = 30 ft
- Length = 250 ft
Calculating the base area:
\[ \text{Base Area} = \text{Width} \times \text{Length} = 30 , \text{ft} \times 250 , \text{ft} = 7500 , \text{ft}^2 \]
Next, the height of the pyramid (the depth of the trench) is given as 15 ft.
Now we can substitute the values into the volume formula:
\[ V = \frac{1}{3} \times 7500 , \text{ft}^2 \times 15 , \text{ft} \] \[ V = \frac{1}{3} \times 112500 , \text{ft}^3 \] \[ V = 37500 , \text{ft}^3 \]
Therefore, the capacity for this trench is 37,500 ft³.
The correct answer is: 37,500 ft.³