Question

Find the approximate change in the volume V of a cube of side x metre caused by increasing the side by 1%.

Answer 1

The volume (V) of a cube of side x is given by $V=x^3$
$\Rightarrow \frac{dV}{dx}=3x^2$ (Differentiate w.r.t,x)
Now, change in volume $\Delta V=\left(\frac{dV}{dx}\right)\Delta x=\left(3x^2\right)\Delta x$
$=3x^2\left(0.01x\right)=0.03x^3$ (as $\Delta x=1\%$ of x = 0.01x)
$=0.03x^3{m}^3$