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)
To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.
First, we need to find the height of the pyramid. This can be done by dividing the width of the opening by 2, and then using the Pythagorean theorem to find the height:
\(a^2 + b^2 = c^2\)
\((15)^2 + (250/2)^2 = h^2\)
\(225 + 31250 = h^2\)
\(31575 = h^2\)
\(h ≈ 178.1 ft\)
Now, we can calculate the volume of the pyramid using the formula:
\[V = \frac{1}{3} \times \text{Base area} \times \text{Height}\]
\[V = \frac{1}{3} \times (30 \times 250) \times 178.1\]
\[V = \frac{1}{3} \times 7500 \times 178.1\]
\[V ≈ 396250 ft^3\]
Therefore, the capacity of the trench is approximately 396,250 cubic feet.