How many cubic yards of gravel must be purchased for a trench that requires 430 cubic feet?

To find the correct amount of gravel required in cubic yards for a trench that needs 430 cubic feet, it is essential to convert cubic feet to cubic yards because construction materials are often measured in cubic yards.

There are 27 cubic feet in one cubic yard (since 1 yard = 3 feet and 1 cubic yard = 3 feet × 3 feet × 3 feet = 27 cubic feet). To convert cubic feet to cubic yards, divide the volume in cubic feet by 27.

In this case, divide 430 cubic feet by 27:

[

\text{Cubic yards} = \frac{430 \text{ cubic feet}}{27 \text{ cubic feet per cubic yard}} \approx 15.93 \text{ cubic yards}

]

When rounding 15.93 to the nearest whole number, it becomes 16 cubic yards. Therefore, the amount of gravel that must be purchased for the trench is 16 cubic yards, justifying why this choice is the correct answer.