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?

Question

(1 point)

Answer 1

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

The volume of a pyramid is given by the formula:
Volume = (1/3) * base area * height

First, we need to find the base area of the pyramid. The top opening of the trench is 30 ft wide by 250 ft long. So the base area can be calculated as the product of the width and length:
Base Area = 30 ft * 250 ft

Next, we need to find the height of the pyramid. The deepest part in the middle is 15 ft.

Now, we can calculate the volume of the pyramid:
Volume = (1/3) * 30 ft * 250 ft * 15 ft.

Simplifying this expression:
Volume = (1/3) * 112500 ft³ = 37500 ft³.

Therefore, the capacity of the trench is 37500 cubic feet.