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The dimensions of a box are measured to be 18.4 inches by 17.92 inches by 26 inches. The volume of the box can be found by multiplying these three dimensions. What is the volume of the box expressed to the correct number of significant figures?

A. [tex]$8,600 \, in^3$[/tex]
B. [tex]$8,573 \, in^3$[/tex]
C. [tex]$8,572.9 \, in^3$[/tex]
D. [tex]$8,570 \, in^3$[/tex]



Answer :

GinnyAnswer
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].

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