Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.

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%.