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.
Solution:
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 $3 a$.
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