College Physics Problem 1.27

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.


The average area of the room is

A=l times w

A=3.955 m times 3.050 m

A=12.06 m^{2}

Compute for the percent uncertainties of each dimension.

% unc_{width}=frac{0.005 m}{3.050 m} times 100 %=0.1639 %

% unc_{length}=frac{0.005 m}{3.955 m}times100 %=0.1264 %

The percent uncertainty in the area is the combined effect of the uncertainties of the length and width.

% unc_{area}=0.1639%  + 0.1264%

% unc_{area}=0.2903%

The uncertainty in the area is

delta_{area}=frac{0.2903%}{100%}times 12.06 m^{2}

delta_{area}=0.035 m^{2}

Therefore, the area is

12.06 pm 0.035  m^{2}