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The dimensions of the base of Box 1 are:

A. Width: x; Length: 3x
B. Width: x; Length: x + 3
C. Width: x; Length: x - 3
D. Width: x; Length: 3/x

Answer :

Final answer:

To calculate the volume of a rectangular box with given lengths, widths, and heights, multiply the dimensions together. Uncertainty is also factored in via the rules of propagation of uncertainties for each dimension to get the total uncertainty in the volume.

Explanation:

Calculating the volume of a rectangular box requires multiplying its length, width, and height. For a box with sides measuring 1.80 cm, 2.05 cm, and 3.1 cm, the volume is calculated by multiplying these dimensions together:

Volume = Length × Width × Height = 1.80 cm × 2.05 cm × 3.1 cm = 11.4 cm³.

To include the uncertainty in the measurements, it is necessary to apply the rules of propagation of uncertainties. Since each dimension has an uncertainty (e.g., ±0.01 cm for the length), these must be accounted for by using the partial derivative of the volume with respect to each dimension, multiplied by the uncertainty of that dimension. The uncertainties are combined to give the total uncertainty of the volume.

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