Question

Question

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)
Responses

112,500 ft.3
112,500 feet cubed

337,500 ft.3
337,500 feet cubed

37,500 ft.3
37,500 feet cubed

98.33 ft.3
98.33 feet cubed

Answer 1

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

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

In this case:

1. The base area is the area of the top opening, which is given as 30 ft wide by 250 ft long: \[ \text{Base Area} = 30 , \text{ft} \times 250 , \text{ft} = 7500 , \text{ft}^2 \]

2. The height is the depth of the trench, which is given as 15 ft.

Now, we can substitute these values into the volume formula: \[ \text{Volume} = \frac{1}{3} \times 7500 , \text{ft}^2 \times 15 , \text{ft} \]

Calculating this gives: \[ \text{Volume} = \frac{1}{3} \times 7500 \times 15 = \frac{112500}{3} = 37500 , \text{ft}^3 \]

Therefore, the capacity for the trench is:

\[ \boxed{37,500 , \text{ft}^3} \]