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.

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

$V=x^{3}$

We have

$\frac{\Delta x}{x} \times 100=a$

$\therefore \frac{d V}{d x}=3 x^{2}$

$\Rightarrow \frac{\Delta V}{V}=\frac{3 x^{2}}{V} d x=\frac{3 x^{2}}{x^{3}} \times \frac{a x}{100}$

$\Rightarrow \frac{\Delta V}{V} \times 100=3 a$

Hence, the percentage error in the volume is $3 a$.