Final answer:
To find the area of the rectangular room, multiply the length by the width to get 12.06275 square meters. To calculate the uncertainty, add the relative uncertainties and apply the total relative uncertainty to the area, which results in ±0.035 square meters.
Step-by-step explanation:
The dimensions of a rectangular room are given as the length being 3.955 ± 0.005 m and the width being 3.050 ± 0.005 m. To calculate the area of the room, you would use the formula for the area of a rectangle, which is length multiplied by width. Thus, the area would be:
Area = Length × Width = 3.955 m × 3.050 m = 12.06275 square meters
To calculate the uncertainty in the area, you need to consider the maximum possible deviation for both the length and the width. The rule for multiplication when combining uncertainties is to add the relative uncertainties. The calculated maximum relative uncertainty for the area will then be applied to the measured area:
Relative uncertainty of length = ±0.005 m / 3.955 m = 0.00126 (or 0.126%)
Relative uncertainty of width = ±0.005 m / 3.050 m = 0.00164 (or 0.164%)
Total relative uncertainty = 0.00126 + 0.00164 = 0.00290 (or 0.29%)
Total uncertainty of the area = 0.00290 × 12.06275 m2 = ±0.03498 m2, which we can round to ±0.035 m2 for simplicity.
Therefore, the area of the room with its uncertainty is 12.06275 ± 0.035 square meters.