To solve the problem and find the volume of the box expressed to the correct number of significant figures, follow these steps:
1. Identify the Measurements:
- Length: 18.4 inches (3 significant figures)
- Width: 17.92 inches (4 significant figures)
- Height: 26 inches (2 significant figures)
2. Calculate the Volume:
- Volume = Length × Width × Height
- Volume = 18.4 inches × 17.92 inches × 26 inches
- Performing the multiplication: Volume ≈ 8572.928 cubic inches
3. Determine the Correct Number of Significant Figures:
- When multiplying, the result should be reported with the same number of significant figures as the measurement with the fewest significant figures.
- Among the given measurements, the height (26 inches) has the fewest significant figures, which is 2.
4. Round the Volume to the Correct Number of Significant Figures:
- The unrounded volume is 8572.928 cubic inches.
- Rounding this to 2 significant figures involves looking at the first two significant digits and rounding accordingly: 8572.928 rounds to 8600 cubic inches.
Therefore, the volume of the box expressed to the correct number of significant figures is:
A. [tex]$8600 \, \text{in}^3$[/tex].
