Question

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

a) Area: 12.06 m², Uncertainty: 0.041 m²
b) Area: 12.06 m², Uncertainty: 0.1 m²
c) Area: 12.06 m², Uncertainty: 0.021 m²
d) Area: 12.06 m², Uncertainty: 0.042 m²

Answer 1

The area of the rectangular room is 12.08275 m² with an uncertainty of 0.0155 m².

Step-by-step explanation:

To calculate the area of a rectangular room, you multiply its length by its width. In this case, the length of the room is 3.955 m and the width is 3.050 m.

The area of the room is: 3.955 m * 3.050 m = 12.08275 m².

To find the uncertainty in the area, we add the uncertainties in the length and width. The uncertainty in the length is 0.005 m and in the width is also 0.005 m.

Therefore, the uncertainty in the area is: 0.005 m * 3.050 m + 0.005 m * 3.955 m = 0.0155 m².