Answer :

Given the error in the measurement of the edge of a cubical box is 1%.


Let x be the edge of the cubical box, and Δx is the error in the value of x.


Hence, we have


Δx = 0.01x


The surface area of a cubical box of radius x is given by


S = 6x2


On differentiating A with respect to x, we get




We know




Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 0.01x


ΔS = (12x)(0.01x)


ΔS = 0.12x2


The percentage error is,



Error = 0.02 × 100%


Error = 2%


Thus, the error in calculating the surface area of the cubical box is 2%.


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