#### Question

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is

(a) 2*a*%

(b)\[\frac{a}{2} \%\]

(c) 3*a*%

(d) none of these

#### Solution

(a) 2*a*%

Let *x* be the side of the cube and *y* be its surface area.

\[\frac{∆ x}{x} \times 100 = a\]

\[\text { Also }, y = 6 x^2 \]

\[ \Rightarrow \frac{dy}{dx} = 12x\]

\[ \Rightarrow \frac{∆ y}{y} = \frac{12x}{y} \times dx = \frac{2}{x} \times \frac{ax}{100}\]

\[ \Rightarrow \frac{∆ y}{y} \times 100 = 2a\]

\[\text { Hence, the error in the surface area is} 2a % .\]

Is there an error in this question or solution?

Solution If There is an Error of A% in Measuring the Edge of a Cube, Then Percentage Error in Its Surface is (A) 2a% (B) a 2 %(C) 3a% (D) None of These Concept: Approximations.