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)

Question

Responses

112,500 ft.3

98.33 ft.3

337,500 ft.3

37,500 ft.3

Answer 1

To find the capacity of the trench, we need to calculate the volume of the upside-down rectangular pyramid.

The formula for the volume of a rectangular pyramid is:

Volume = (1/3) * base area * height

First, let's calculate the base area of the pyramid. The top opening is given as 30 ft wide by 250 ft long. So the base area is:

Base area = 30 ft * 250 ft = 7500 ft²

Next, let's calculate the height of the pyramid. The deepest part in the middle is given as 15 ft.

Height = 15 ft

Now, let's plug these values into the formula to find the volume:

Volume = (1/3) * 7500 ft² * 15 ft
= 112,500 ft³

Therefore, the capacity for this trench is 112,500 ft³. The correct answer is:

112,500 ft.³