To determine the volume of the box and express it in the correct number of significant figures, follow these steps:
1. Calculate the Volume:
The dimensions of the box are provided as 18.4 inches, 17.92 inches, and 26 inches. The volume [tex]\( V \)[/tex] of a box is given by the formula:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
So, the volume is:
[tex]\[
V = 18.4 \times 17.92 \times 26 = 8572.928 \, \text{in}^3
\][/tex]
2. Identifying Significant Figures:
Significant figures in a number are the digits that carry meaningful contributions to its precision. In this problem, the dimensions have the following significant figures:
- 18.4 has 3 significant figures
- 17.92 has 4 significant figures
- 26 has 2 significant figures
When multiplying numbers, the result should be expressed with as many significant figures as the measurement with the least number of significant figures. In this case, the number with the least significant figures is 18.4 (3 significant figures).
3. Rounding to the Correct Number of Significant Figures:
The calculated volume is 8572.928 in[tex]\(^3\)[/tex]. To match the least number of significant figures (3 significant figures), we need to round 8572.928 appropriately.
- The first three digits are 857, and the next digit is 2.
- Since 2 is less than 5, we round down, resulting in the nearest number with 3 significant figures: 8570.
Thus, the volume of the box, expressed to the correct number of significant figures, is:
D. [tex]\(8,570 \, \text{in}^3\)[/tex]
