Q. 45.0( 2 Votes )
Find the percenta
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
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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