A construction company is dogging a drainage trench it makes the shape of an upside down rectangular pyramid the top opening will be 30 ft wide by 250 feet long and the deepest part in the middle will be 15 feet what is the capacity for this trench
To find the capacity of the trench, we need to calculate the volume.
First, let's find the width and length of the bottom opening of the upside-down rectangular pyramid.
The bottom opening of the trench is the same size as the top opening, which is 30 ft wide and 250 ft long.
Now, let's find the average width and length of the top and bottom openings of the trench.
Average width = (Bottom width + Top width) / 2
= (30 ft + 30 ft) / 2
= 30 ft
Average length = (Bottom length + Top length) / 2
= (250 ft + 250 ft) / 2
= 250 ft
Now, let's find the average height of the trench.
Average height = (Deepest height + 0) / 2
= (15 ft + 0 ft) / 2
= 7.5 ft
The formula to find the volume of an upside-down rectangular pyramid is given by:
Volume = (1/3) × Average width × Average length × Average height
Plugging in the values, we can calculate the volume:
Volume = (1/3) × 30 ft × 250 ft × 7.5 ft
= 3,750 ft^3
Therefore, the capacity for this trench is 3,750 cubic feet.