Question

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2\%$.

• A. $1.06x^3{m}^3$
• B. $1.26x^3{m}^3$
• C. $2.50x^3{m}^3$
• D. $0.06x^3{m}^3$

Answer 1

Answer: (D)

It is given that $\frac{\Delta x}{x}\times 100=2$
We have, $V=x^3$
$\Rightarrow \frac{dV}{dx}=3x^2$
$\therefore \Delta V=\frac{dV}{dx}\times \Delta x$
$\Rightarrow \Delta V=3x^2\Delta x$
$\Rightarrow \Delta V=3x^2\times \frac{2x}{100}$
$\Rightarrow \Delta V=0.06x^2$
Thus, the approximate change in volume is $0.06x^3{m}^3$.