To determine the correct volume of the box and express it to the appropriate number of significant figures, follow these steps:
1. Determine the volume:
The volume ([tex]\(V\)[/tex]) of a rectangular box is calculated by the formula:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given the dimensions:
- Length = 18.4 inches
- Width = 17.92 inches
- Height = 26 inches
Multiplying these dimensions gives:
[tex]\[
V = 18.4 \times 17.92 \times 26
\][/tex]
2. Volume Calculation:
The calculation yields a volume value:
[tex]\[
V \approx 8572.928 \text{ cubic inches}
\][/tex]
3. Determine significant figures:
The given measurements of length, width, and height have the following significant figures:
- 18.4 has 3 significant figures
- 17.92 has 4 significant figures
- 26 has 2 significant figures
The result should be rounded to the smallest number of significant figures in the given measurements, which is 2 significant figures.
4. Round the volume to 2 significant figures:
To round 8572.928 to 2 significant figures:
- The first two significant figures are '85'.
- The digit following '85’ is '7’, which is greater than 5, so we round up the second digit.
Thus, 8572.928, rounded to 2 significant figures, is:
[tex]\[
8600 \text{ cubic inches}
\][/tex]
Therefore, the correct answer is:
A. 8,600 in [tex]\( \text{in}^3 \)[/tex]
