If a trench is 526 feet long, 4.0 feet wide, and 5.5 feet deep, how many cubic yards of soil were excavated?

To calculate the volume of soil excavated from the trench, you first determine the volume in cubic feet and then convert that to cubic yards.

The formula for the volume of a rectangular prism (which is the shape of the trench) is:

Volume = Length × Width × Depth.

In this case, the trench has a length of 526 feet, a width of 4.0 feet, and a depth of 5.5 feet. Plugging these values into the formula gives:

Volume = 526 ft × 4.0 ft × 5.5 ft.

Calculating this step-by-step:

1. First, 526 feet times 4.0 feet equals 2104 square feet.

2. Next, multiply 2104 square feet by 5.5 feet, which equals 11572 cubic feet.

Now, to convert cubic feet to cubic yards, you need to remember that 1 cubic yard equals 27 cubic feet. Therefore, to convert:

11572 cubic feet ÷ 27 cubic feet per cubic yard = approximately 428.61 cubic yards.

When rounded, this would be approximately 430 cubic yards, which aligns with the correct answer. Thus, the calculated volume of soil excavated