Question

The length and width of a rectangular room are measured to be 3.955±0.005m and 3.050±0.005m. Calculate the area of the room and its uncertainty in square meters.

a) 12.0245±0.025m²


b) 12.0245±0.040m²


c) 15.2025±0.025m²


d) 15.2025±0.040m²

Answer 1

The area of the rectangular room is 12.05275 m² with an uncertainty of ± 0.010 m².

Step-by-step explanation:

To calculate the area of the rectangular room, you need to multiply its length by its width. The length is given as 3.955 ± 0.005 m and the width is given as 3.050 ± 0.005 m. The area is therefore (3.955 m)(3.050 m) = 12.05275 m². To find the uncertainty in the area, you need to sum the uncertainties in length and width, which are both ± 0.005 m. Therefore, the area has an uncertainty of ± 0.010 m².