Question

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

Answer 1

The area of the room and its uncertainty in square meters is:

15.642±0.040
`m^2`

Explanation:

We know the area of a rectangular room is the multiplication of the length and width:

`Area= 3.955m*3.955m\\Area= 15.642 m^2`

Now we need to know the uncertainty, the uncertainty of a multiplication is:

`(δ_a)/(|Area|) =(δ_L)/(|L|)+(δ_W)/(|W|)` (1)

`δ_A`: Area uncertainty

`δ_L`: Length uncertainty

`δ_W`: Width uncertainty

A: Area of the room

L: Length

W: Width

Clearing the uncertainty of the area:

`δ_A=((δ_x)/(|x|)+(δ_y)/(|y|))*Area` (2)

`δ_A=((0.005)/(|3.955|)+(0.005)/(|3.955|))*15.642 m^2`

`δ_A= 0.040 m^2`

The area of the room and its uncertainty in square meters is:

15.642±0.040
`m^2`