Final answer:
To calculate the area of a rectangle, multiply the length and width. For a room measuring 3.955 ± 0.005 m by 3.050 ± 0.005 m, the area is 12.1 m² with an uncertainty of ± 0.035 m².
Step-by-step explanation:
To calculate the area of a rectangular room with the given dimensions, you simply multiply the length by the width. In this case, if the rectangle wall has dimensions 23 ft by an unknown width, we would need the width to proceed. However, using the examples provided, the area of a rectangle with dimensions 3.955 ± 0.005 m (length) and 3.050 ± 0.005 m (width) would be calculated by multiplying these two measurements. The area calculation is 3.955 m * 3.050 m = 12.06275 m². To express the result with the correct number of significant figures, we'd report the area as 12.1 m², assuming all figures are significant.
Calculating the uncertainty involves using the maximum possible error in the measurements due to precision limitations. The formula for the uncertainty in a product (area, in this case) is given by the relative uncertainties of the measurements added together. For the given measurements, the uncertainty calculation would be:
- Uncertainty in length: (0.005/3.955)*100% = 0.126% of the length
- Uncertainty in width: (0.005/3.050)*100% = 0.164% of the width
- Combined uncertainty percentage: 0.126% + 0.164% = 0.290%
Applied to the calculated area of 12.06275 m², an uncertainty of 0.290% would give an absolute uncertainty of approximately 0.035 m². Therefore, the area with its uncertainty would be 12.06275 ± 0.035 m², which can be rounded to 12.1 ± 0.035 m² to match the significant figures of the original measurements.