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प्रश्न
A piece of ice is in the form of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume ?
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उत्तर
Let x be the side and V be the volume of the cube.
\[V = x^3 \]
\[\text { We have }\]
\[\frac{∆ x}{x} \times 100 = a\]
\[ \therefore \frac{dV}{dx} = 3 x^2 \]
\[ \Rightarrow \frac{∆ V}{V} = \frac{3 x^2}{V}dx = \frac{3 x^2}{x^3} \times \frac{ax}{100}\]
\[ \Rightarrow \frac{∆ V}{V} \times 100 = 3a\]
\[\text { Hence, the percentage error in the volume is } 3a .\]
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