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

98.33 ft.3
98.33 feet cubed

112,500 ft.3
112,500 feet cubed

37,500 ft.3
37,500 feet cubed

337,500 ft.3
337,500 feet cubed

Answer 1

To calculate the capacity of the trench shaped like an upside-down rectangular pyramid, we can use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

1. Calculate the base area: The base of the pyramid is the top opening (30 ft wide and 250 ft long):

   \[ \text{Base Area} = \text{Width} \times \text{Length} = 30 , \text{ft} \times 250 , \text{ft} = 7500 , \text{ft}^2 \]

2. Determine the height: The height of the pyramid corresponds to how deep the trench is. Here, the depth is given as 15 ft.

3. Calculate the volume: Plugging the values into the volume formula:

   \[ V = \frac{1}{3} \times 7500 , \text{ft}^2 \times 15 , \text{ft} \]

   \[ V = \frac{1}{3} \times 112500 , \text{ft}^3 \]

   \[ V = 37500 , \text{ft}^3 \]

Therefore, the capacity for the trench is 37,500 ft³.

Thus, the correct response is:

37,500 ft.³.