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White raven [17]
3 years ago
8

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 i

n square meters.
Mathematics
1 answer:
Margarita [4]3 years ago
6 0

Answer:

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

15.642±0.040 m^2

Step-by-step 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:

\frac{δ_a}{|Area|} =\frac{δ_L}{|L|}+\frac{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=(\frac{δ_x}{|x|}+\frac{δ_y}{|y|})*Area (2)

δ_A=(\frac{0.005}{|3.955|}+\frac{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

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