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)
• 98.33 ft.3
• 37, 500 ft.*
• 112, 500 ft.$
• 337, 500 ft.*

Answer 1

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

First, let's find the height of the pyramid. The deepest part in the middle is 15 ft. Since the pyramid is upside-down, the height is negative, so the height of the pyramid is -15 ft.

Next, we can find the volume of the pyramid using the formula:
Volume = (1/3) * length * width * height

Plugging in the given values, we get:
Volume = (1/3) * 30 ft * 250 ft * (-15 ft)
= 7500 ft^3 * (-15 ft)
= -112,500 ft^3

The correct answer is 112,500 ft^3.

Therefore, the correct option is:
• 112, 500 ft³