Question

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

Options

• 2a%

• \[\frac{a}{2} \%\]

• 3a%

• none of these

Answer 1

(a) 2a%
Let x be the side of the cube and y be its surface area.

\[\frac{∆ x}{x} \times 100 = a\]

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

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

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

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

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