Question

the length and width of a rectangular room are measured to be 3.955 plus-or-minus 0.005 m by 3.050 plus-or-minus 0.005 m. what is the area of the room and its uncertainty in square meters?

Answer 1

Explanation:

To calculate the area of the room, we multiply its length by its width.

Length = 3.955 m +/- 0.005 m

Width = 3.050 m +/- 0.005 m

Area = Length x Width

Area = (3.955 m)(3.050 m)

Area = 12.06275 m²

To find the uncertainty in the area, we need to consider the maximum and minimum possible values for both the length and width.

The maximum length = (3.955 m + 0.005 m) = 3.960 m

The minimum length = (3.955 m - 0.005 m) = 3.950 m

The maximum width = (3.050 m + 0.005 m) = 3.055 m

The minimum width = (3.050 m - 0.005 m) = 3.045 m

Maximum Area = (3.960 m)(3.055 m) = 12.07572 m²

Minimum Area = (3.950 m)(3.045 m) = 12.033 m²

So the area of the room is 12.06275 m² with an uncertainty of +/- 0.04272 m².