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

• 98.33 ft.3
• 337, 500 ft. 3
• 37,500 ft. 3
O 112, 500 ft. 3

Answer 1

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

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

1. Calculate the Base Area:

   • The base area can be calculated by multiplying the width and the length of the top opening. \[ \text{Base Area} = \text{Width} \times \text{Length} = 30 , \text{ft} \times 250 , \text{ft} = 7500 , \text{ft}^2 \]

2. Calculate the Height (Depth):

   • The height of the pyramid (depth of the trench) is given as 15 ft.

3. Calculate the Volume: \[ V = \frac{1}{3} \times 7500 , \text{ft}^2 \times 15 , \text{ft} \] \[ V = \frac{1}{3} \times 112500 , \text{ft}^3 = 37500 , \text{ft}^3 \]

So, the capacity for this trench is:

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