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

Answer 1

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

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

1. **Base Area**: The base of the trench is rectangular with width and length:
- Width = 30 ft
- Length = 250 ft

So, the base area \(A\) is:
\[
A = \text{Width} \times \text{Length} = 30 \, \text{ft} \times 250 \, \text{ft} = 7500 \, \text{ft}^2
\]

2. **Height**: The deepest part of the trench is 15 ft, which will act as the height \(h\) of the pyramid:
\[
h = 15 \, \text{ft}
\]

3. **Calculating the Volume**:
We can now substitute the values into the volume formula:
\[
\text{Volume} = \frac{1}{3} \times 7500 \, \text{ft}^2 \times 15 \, \text{ft} = \frac{1}{3} \times 112500 \, \text{ft}^3 = 37500 \, \text{ft}^3
\]

Thus, the capacity for this trench is **37,500 ft.³**.

The correct response is:

**37,500 ft.³**.