For a 15' by 30' paver patio with a finished depth of 6", how many cubic yards of soil must be excavated?

To determine the amount of soil that must be excavated for the paver patio, first, you need to calculate the volume of the area that needs to be dug out. The formula to find the volume of a rectangular prism (the shape of the excavation area) is length × width × depth.

The dimensions of the patio are given as 15 feet by 30 feet with a depth of 6 inches. To perform the calculation, we first need to convert all measurements to the same unit. Since the dimensions are in feet, we convert the depth of 6 inches into feet by dividing by 12 (since there are 12 inches in a foot). This gives us a depth of 0.5 feet.

Now, using the formula:

Volume = Length × Width × Depth

Volume = 15 feet × 30 feet × 0.5 feet

Volume = 225 cubic feet.

Next, we need to convert cubic feet to cubic yards since landscaping materials are often measured in cubic yards. There are 27 cubic feet in a cubic yard (3 feet × 3 feet × 3 feet).

To convert cubic feet to cubic yards, we divide the volume in cubic feet by 27:

225 cubic feet ÷