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 ?
To find the capacity of the trench, we need to calculate the volume of the trench in cubic feet.
Since the shape of the trench is an upside-down rectangular pyramid, the volume can be calculated using the formula:
Volume = 1/3 × length × width × height
First, we need to calculate the average width of the top and bottom of the trench:
Average width = (30 ft + 250 ft) / 2 = 140 ft
Next, we can plug in the values into the formula:
Volume = 1/3 × 140 ft × 250 ft × 15 ft
Volume = 1/3 × 5,250,000 ft^3
Volume = 1,750,000 ft^3
Therefore, the capacity of the drainage trench is 1,750,000 cubic feet.