Answer:
Let x be the length of an of edge of the cube. Then, its volume y is given by \[y={{x}^{3}}.\] Let \[\Delta x\]be error in x and \[\Delta y\] be the corresponding error in y. Then, \[\Delta y=\frac{dy}{dx}\Delta x\]\[\Rightarrow \] \[\Delta y=3{{x}^{2}}\Delta x\] \[\Rightarrow \] \[\frac{\Delta y}{y}\times 100=\frac{3{{x}^{2}}}{y}\Delta x\times 100\] \[\frac{3{{x}^{2}}}{{{x}^{3}}}\Delta x\times 100=3\left( \frac{\Delta x}{x}\times 100 \right)\] = 3% \[\left[ \because \frac{\Delta x}{x}\times 100=1,\,\text{given} \right]\]
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