To perform the indicated operation and express the final answer with the correct number of significant figures, follow these steps:

1. Convert units to be consistent:

   • Convert 0.556 feet to inches: $0.556 \, \text{ft} \times 12 \, \text{in/ft} = 6.672 \, \text{in}$

2. Perform the multiplication: $7.425 \, \text{in} \times 6.672 \, \text{in} \times 9.449 \, \text{in} = 468.7085264 \, \text{in}^3$

3. Determine the correct number of significant figures:

   • The original numbers have the following significant figures:
     • 7.425 has 4 significant figures.
     • 6.672 (converted from 0.556) has 3 significant figures.
     • 9.449 has 4 significant figures.
   • The final answer should be expressed to the lowest number of significant figures, which is 3.

4. Round the result to 3 significant figures: $468.7085264 \, \text{in}^3 \approx 469 \, \text{in}^3$

Final Answer:

$469 \, \text{in}^3$

Would you like more details or have any questions? Here are some related questions:

1. What are significant figures, and why are they important?
2. How do you convert between different units of measurement?
3. What is the process for determining the number of significant figures in a final answer?
4. How would this problem change if the dimensions were given in meters instead of inches and feet?
5. Can you explain how to round numbers correctly when dealing with significant figures?

Tip: Always ensure units are consistent before performing any calculations, especially in problems involving multiplication or division of measurements.