The appropriate change in the volume V of a cube of side x metres caused by increasing the side by 2% is :
Answer & explanation
Correct answer: option 1
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