Final answer:
The area of a rectangular room measuring 3.955 ± 0.005 m by 3.050 ± 0.005 m is 12.063 m². The uncertainty in the area is 0.0105 m², calculated by taking the difference between the maximum and minimum possible areas and dividing by two.
Step-by-step explanation:
To calculate the area of a rectangular room with the dimensions 3.955 ± 0.005 m by 3.050 ± 0.005 m, you would multiply the length and width. The area is defined as the product of the two dimensions. The calculation would be as follows:
Area = length × width
= 3.955 m × 3.050 m
= 12.06275 m²
We can round this to 12.063 m² to match the number of significant figures given in the dimensions.
To calculate the uncertainty of the area, we first need to calculate the maximum possible area and the minimum possible area using the given uncertainties and then find the difference from the calculated area.
Maximum area = (3.955 + 0.005) m × (3.050 + 0.005) m
= 12.073 m²
Minimum area = (3.955 - 0.005) m × (3.050 - 0.005) m
= 12.052 m²
The uncertainty in the area would be half the difference between the maximum and minimum areas, which we can express as:
Uncertainty = (12.073 m² - 12.052 m²) / 2
= 0.0105 m²
So the area of the room with its uncertainty is 12.063 m² ± 0.0105 m².