## Problem 3:Determine the area of a rectangular sheet with length (l ± Δl) = (1.50 ± 0.02) m and width (w ± Δw) = (0.20 ± 0.01) m. Calculate area (A ± ΔA).

Solution

Given Data

Length of the sheet, l ± Δl = (1.50 ± 0.02) m Width of the sheet, w ± Δw = (0.20 ± 0.01) m

Area of the sheet with uncertainty, A ± ΔA

Concept: Area is the product of length and width. Therefore, in calculation of area, we should know about the product rule of uncertainty. It states, in case of product, the percentage uncertainties of the terms to be multiplied (length and width in this case) are added. So, first we find the percent uncertainties in the measurement of length and breadth of the rectangular sheet. Then we will add the sum of these percentage uncertainties with the product of the length and width. This will give us the percentage uncertainty of the area. Then we convert the percentage uncertainty in fractional uncertainty and add with the product. Therefore,

Percentage uncertainty in length, Percentage uncertainty in width, According to product rule, percentage uncertainty in the area of the sheet will be the sum of percentage uncertainties of length and width. Therefore, percentage uncertainty in the area, Area of the sheet with percentage uncertainty is, Now we convert this to fractional uncertainty.  