The sides of a small rectangular box are measured to be 1.80±0.01cm, 2.05±0.02cm, and 3.1±0.1 cm long. calculate its volume and uncertainty in cubic centimeters.

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54

Step-by-step explanation:

We know the volume of a rectangular box is the multiplication of the sides:

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

(1)

Where:

: Volume uncertainty

: Side 1 uncertainty (0.01cm)

: Side 2 uncertainty (0.02cm)

: Side 3 uncertainty (0.10cm)

: Side 1 (1.80cm)

: Side 2 (2.05cm)

: Side 3 (3.10cm)

Clearing the uncertainty of the volume:

(2)

The volume of the rectangular box and its uncertainty in cubic centimeters is:

11.44±0.54

answer: -2+√x,-2-√x

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