If 45 cubic yards excavated turns into 36 cubic yards when compacted, what is the percentage difference?

To determine the percentage difference in volume between the excavated and compacted material, it is essential to analyze how much the volume has decreased during the compaction process.

First, calculate the reduction in volume: 45 cubic yards (excavated) minus 36 cubic yards (compacted) equals a difference of 9 cubic yards.

Next, to find the percentage difference, divide the reduction in volume (9 cubic yards) by the original volume (45 cubic yards) and then multiply by 100 to express it as a percentage:

[

\text{Percentage Difference} = \left( \frac{\text{Reduction}}{\text{Original Volume}} \right) \times 100 = \left( \frac{9}{45} \right) \times 100 = 20%

]

Thus, the percentage difference between the excavated volume and the compacted volume is 20%. This method provides a clear understanding of how compaction affects material volume, which is a key concept in excavation and grading practices.