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------------------------------------------------ Find the uncertainty of the surface area of a closed rectangular box given by the formula [tex]SA = 2(lw + dl + dw)[/tex], where $ l $ is the length, $ d $ is the depth, and $ w $ is the width.

Show your solution.

To find the uncertainty of the surface area of a closed rectangular box, calculate the uncertainties of each dimension and use the formula 2(lw+dl+dw) to find the uncertainty in the surface area.

Explanation:

To find the uncertainty of the surface area of a closed rectangular box, we need to calculate the uncertainty of each dimension and then use the formula to find the uncertainty in the surface area. Let's say the uncertainties of length, depth, and width are Δl, Δd, and Δw respectively. The uncertainty of the surface area (ΔSA) can be calculated as:

ΔSA = 2(Δl * w + l * Δw + Δl * Δw)

For example, if the length is 10 cm with an uncertainty of 0.2 cm, the width is 5 cm with an uncertainty of 0.1 cm, and the depth is 3 cm with an uncertainty of 0.05 cm, we can substitute these values into the formula to find the surface area and uncertainty.

To calculate the absolute uncertainty, we add the relative uncertainties in each term and multiply them by the corresponding values. Finally, we add all the terms together to get the uncertainty of the surface area.

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