To find the length of the smaller piece of wood after Lucy saws the rod, you can subtract the length of the larger piece from the original length of the rod.
Original rod length: 918 inches
Larger piece length: 734 inches
Now, subtract the length of the larger piece from the original length:
\[ \text{Smaller piece length} = \text{Original rod length} - \text{Larger piece length} \]
\[ \text{Smaller piece length} = 918 - 734 = 184 \text{ inches} \]
Now let's check the available answers. None seem to match 184 inches exactly, so none of the provided options are correct. Please recheck your data or the choices available.