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.
$$\begin{gathered} V=x^3 \\ \mathrm{We}\mathrm{have} \\ \frac{∆x}{x}\times 100=a \\ \therefore \frac{dV}{dx}=3x^2 \\ \Rightarrow \frac{∆V}{V}=\frac{3x^2}{V}dx=\frac{3x^2}{x^3}\times \frac{ax}{100} \\ \Rightarrow \frac{∆V}{V}\times 100=3a \\ \mathrm{Hence},\mathrm{the}\mathrm{percentage}\mathrm{e}\mathrm{rror}\mathrm{in}\mathrm{the}\mathrm{volume}\mathrm{is}3a. \end{gathered}$$