To determine the volume of the box and express it to the correct number of significant figures, follow these steps carefully:
1. Identify the Dimensions:
- Dimension 1: [tex]\( 18.4 \)[/tex] inches
- Dimension 2: [tex]\( 17.92 \)[/tex] inches
- Dimension 3: [tex]\( 26 \)[/tex] inches
2. Calculate the Volume:
- Multiply the three dimensions together:
[tex]\[
\text{Volume} = 18.4 \times 17.92 \times 26
\][/tex]
- When you do the multiplication, you get:
[tex]\[
\text{Volume} = 8572.928 \text{ cubic inches}
\][/tex]
3. Determine Significant Figures:
- Check the number of significant figures in each dimension:
- [tex]\( 18.4 \)[/tex] has 3 significant figures.
- [tex]\( 17.92 \)[/tex] has 4 significant figures.
- [tex]\( 26 \)[/tex] has 2 significant figures.
- The volume should be expressed with the least number of significant figures from the given measurements, which is 2 significant figures (from [tex]\( 26 \)[/tex]).
4. Round the Volume:
- Rounding [tex]\( 8572.928 \)[/tex] to 2 significant figures:
[tex]\[
8572.928 \approx 8570
\][/tex]
- Therefore, the volume rounded to the correct number of significant figures is [tex]\( 8570 \)[/tex] cubic inches (sometimes written as [tex]\( 8.57 \times 10^3 \)[/tex]).
So, the correct answer is:
D. [tex]\( 8,570 \, \text{in}^3 \)[/tex]
