Question

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 ?

Answer 1

Let x be the side and V be the volume of the cube.

\[V = x^3 \]

\[\text { We have }\]

\[\frac{∆ x}{x} \times 100 = a\]

\[ \therefore \frac{dV}{dx} = 3 x^2 \]

\[ \Rightarrow \frac{∆ V}{V} = \frac{3 x^2}{V}dx = \frac{3 x^2}{x^3} \times \frac{ax}{100}\]

\[ \Rightarrow \frac{∆ V}{V} \times 100 = 3a\]

\[\text { Hence, the percentage error in the volume is } 3a .\]