Final answer:
To evaluate the error in the area of a piece of cloth with given dimensions, calculate the nominal area, find the percent uncertainties for length and width and sum them to give total percent uncertainty. Applying the percent uncertainty to the nominal area gives the maximum possible error, which is ±0.26m².
Step-by-step explanation:
The question is asking to evaluate the error in the area of a piece of cloth, given the length is (4.8±0.3)m and the width is (6.6±0.2)m. To find the maximum possible error in the area, we will use the concept of percent uncertainties and apply it to the multiplication of the length and width to get the area.
The area of the rectangle is calculated by multiplying the length by the width. First, let's find the nominal area:
A = length × width = 4.8m × 6.6m = 31.68m²
Now, we calculate the percentages of the uncertainties:
- Percent uncertainty of the length = (0.3 / 4.8) × 100% = 6.25%
- Percent uncertainty of the width = (0.2 / 6.6) × 100% = 3.03%
The total percent uncertainty for multiplication is the sum of the individual percent uncertainties:
- Total percent uncertainty = 6.25% + 3.03% = 9.28%
Finally, we use the total percent uncertainty to find the maximum error in the area:
Error in area = (9.28% / 100) × 31.68m² = 2.94m²
Since we require the error rounded to the same precision as the calculated area and the options provided, we keep only two significant digits:
Rounded error in area = ±0.26m²
Therefore, the error in the area of a piece of cloth with the given dimensions is ±0.26m², which corresponds to option d.