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.

Answer 1

Answer:

The area of the room is $12.063\pm 0.035m^{2}$

Step-by-step explanation:

Given

Length of room = 3.955 ±0.005 m

width of room = 3.050 ±0.005 m

Now we know that

$Area=length\times width\\\\=(l\pm \Delta l)(w\pm \Delta w)\\\\=l\times w\pm l\times\Delta w\pm w\times \Delta l+\Delta l\times \Delta w\\\\=l\times w\pm (l\times\Delta w+ w\times \Delta l)(\because \Delta l\times \Delta w\approx 0)\\\\\therefore Area = 3.955\times 3.050\pm (3.955\times 0.005+3.050\times 0.005)\\\\\therefore Area=12.063\pm 0.035$