The appropriate change in the volume V of a cube of side x metres caused by increasing the side by 2% is :

$0.06x^3\, m^3$

The correct answer is option (1) → $0.06x^3\, m^3$

$v=x^3$

$dv=3x^2dx$

$dx=\frac{2}{100}x$

so $\frac{dv}{v}=\frac{3x^2dx}{x^3}⇒\frac{3x^2×2x}{100x^3}=\frac{6}{100}$

$\frac{dv}{v}×100=6$

⇒ 6% change

or $0.06x^3$ change