Determine the area of a rectangular sheet with length (I ± Δl) = (1.50 ± 0.02) m and width (w ± Δw) = (0.20 ± 0.01) m. Calculate the area (A + ΔA). (0.30 m², ± 0.02 m²)



Given:

Length of the rectangular sheet = l ± Δ l = (1.50 ± 0.02) m 
Width of the rectangular sheet = w ± Δ w = (0.20 ± 0.01) m 


To Find :

Area of the rectangular sheet = A ± Δ A = ?


Solution:

For the product percentage uncertainties as added. So, converting the fractional uncertainty to percentage uncertainty
l ± Δ l = (1.50 ± 0.02) m  = (1.50 ± `\frac {0.02}{1.50}`ｘ100) m = (1.5 ± 1.333 % ) m
w ± Δ w = (0.20 ± 0.01) m  = (0.20 ± `\frac {0.01}{0.20}`ｘ100) m = (0.20 ± 5.0 %) m 

Since the area of the rectangle is the product of length and width,

A ± Δ A = length ｘ width 

A ± Δ A = (l ± Δ l) ｘ (w ± Δ w) 

A ± Δ A = (1.5 ± 1.333 % ) m ｘ (0.20 ± 5.0 %) m 

The percentage uncertainties are added in product. So,

A ± Δ A = (1.5 )(0.20) ± (1.333 % + 5.0 %) m²

A ± Δ A = (0.3 ± 6.333 %) m²

or ( converting from % uncertainty to fractional uncertainty)

A ± Δ A = (0.3 ± 6.333 %) m² = (0.3 ± `\frac {6.333}{100}`ｘ0.3) m² = (0.30 ± 0.0189 %) m² 

A ± Δ A = (0.30 ± 0.02 ) m²

or

A ± Δ A = 0.30 m² ± 0.02 m² ------------Ans

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