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
Answers to this quick check are-
1. 720
2. 9,403.33
3. 296,874.67
4.880
5.37,500
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To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.
The volume of an upside-down rectangular pyramid can be calculated using the formula:
V = (1/3) * B * h
where V is the volume, B is the area of the base, and h is the height of the pyramid.
In this case, the base of the pyramid is a rectangle with dimensions 30 ft wide by 250 ft long. Thus, the area of the base is:
B = length * width = 30 ft * 250 ft = 7500 ft^2
The height of the pyramid is given as 15 ft.
Plugging these values into the formula, we get:
V = (1/3) * 7500 ft^2 * 15 ft
V = 37500 ft^3
Therefore, the capacity of the trench is 37500 cubic feet.
To find the capacity of the trench, we need to calculate its volume. The volume of an upside down rectangular pyramid can be found using the formula:
Volume = (1/3) * base area * height
Given:
Width of the top opening = 30 ft
Length of the top opening = 250 ft
Depth at the middle = 15 ft
First, we need to calculate the area of the rectangle at the top of the trench:
Area = length * width
= 250 ft * 30 ft
= 7500 sq ft
Next, we calculate the base area of the trench, which is the same as the area at the top:
Base area = 7500 sq ft
Then, we need to calculate the height of the trench, which is the depth at the middle:
Height = 15 ft
Now, we can calculate the volume of the trench:
Volume = (1/3) * base area * height
= (1/3) * 7500 sq ft * 15 ft
= (1/3) * 112,500 cu ft
= 37,500 cu ft
Therefore, the capacity of the drainage trench is 37,500 cubic feet.