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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