Thomas needs to cut a piece of wood for a model airplane he is builing. He has four peices of wood: 5 ft, 4 ft, 6 ft, 3 ft long. If the length of wood he needs to cut √11 ft long, which peice of wood should be cut to have the least amount of unused wood.

4 foot

To determine which piece of wood should be cut to have the least amount of unused wood, we need to find the piece of wood that is closest in length to √11 ft.

To do this, we will compare the difference between the length of each piece of wood and √11 ft. The piece of wood with the smallest difference will be the one to cut.

1. Calculate the difference between √11 ft and each piece of wood:
- For the 5 ft piece of wood: |√11 - 5| = |3.316 - 5| = |-1.684| = 1.684 ft
- For the 4 ft piece of wood: |√11 - 4| = |3.316 - 4| = |-0.684| = 0.684 ft
- For the 6 ft piece of wood: |√11 - 6| = |3.316 - 6| = |-2.684| = 2.684 ft
- For the 3 ft piece of wood: |√11 - 3| = |3.316 - 3| = |0.316| = 0.316 ft

2. Compare the differences:
- The difference for the 5 ft piece of wood is 1.684 ft
- The difference for the 4 ft piece of wood is 0.684 ft
- The difference for the 6 ft piece of wood is 2.684 ft
- The difference for the 3 ft piece of wood is 0.316 ft

Based on the comparisons, the 4 ft piece of wood should be cut, as it is the closest in length to √11 ft. This will result in the least amount of unused wood.

To determine which piece of wood Thomas should cut in order to have the least amount of unused wood, we need to find the piece of wood that is closest in length to √11 ft.

First, let's find the square root of 11 feet:

√11 ≈ 3.316 feet

Now, let's compare this value to the lengths of the available pieces of wood:

- The 5 ft piece of wood is too long, as it would result in excess unused wood.
- The 4 ft piece of wood is also too long.
- The 3 ft piece of wood is not long enough.

Finally, we are left with the 6 ft piece of wood. Although it is slightly longer than √11 ft, it is the closest available option. Therefore, Thomas should cut the 6 ft piece of wood to have the least amount of unused wood.