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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.

User Roar
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1 Answer

5 votes

Answer:

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

User Bedla
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