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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
Solution
(a) 2a%
Let x be the side of the cube and y be its surface area.
\[\frac{∆ x}{x} \times 100 = a\]
\[\text { Also }, y = 6 x^2 \]
\[ \Rightarrow \frac{dy}{dx} = 12x\]
\[ \Rightarrow \frac{∆ y}{y} = \frac{12x}{y} \times dx = \frac{2}{x} \times \frac{ax}{100}\]
\[ \Rightarrow \frac{∆ y}{y} \times 100 = 2a\]
\[\text { Hence, the error in the surface area is} \text{ 2a} .\] %
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