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The length of a rectangle is given as L ± I and its with as W ± w. (a) Show that the uncertainty in its area A is a = Lw + lW. Assume that the uncertainties I and w are small. so that the product lw is very small and you can ignore it. (b) Show that the fractional uncertainty in the area is equal to the sum of the fractional uncertainty in length and the fractional uncertainty in width. (c) A rectangular solid has dimensions L ± I. W ± w, and H ± h. Find the fractional uncertainty in the volume, and show that it equals the sum of the fractional uncertainties in the length width, and height. |
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