The measurement of length and breadth of a rectangle are 'b=(10.0+-0.1)cm' and 'I=(30.0+-0.2)cm' . What is the percentage error in the calculation of area of rectangle
Answers
Given : The measurement of length and breadth of a rectangle are 'b=(10.0+-0.1)cm' and 'I=(30.0+-0.2)cm'
To Find : percentage error in the calculation of area of rectangle
Solution:
z + Δz = (x + Δx)(y + Δy) = xy + x Δy + y Δx + Δx Δy
asΔx and Δy are small hence Δx Δy is ignored
=> z + Δz = xy + x Δy + y Δx
=> Δz = x Δy + y Δx
=> Δz/z = x Δy/xy + y Δx/xy
=> Δz/z = Δy/ y + Δx/x
b= 10.0±0.1
=> Δb/b = 0.1/10 = 0.01
I= 30.0±0.2
=> Δl/l = 0.2/30 =0.0067
A = lb
=> ΔA/A = Δl/l + Δb/b
=> ΔA/A = =0.0067 +0.01
=> ΔA/A = =0.0167
in % = 1.67 %
percentage error in the calculation of area of rectangle = 1.67 %
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