Question

Find the approximate change in the volume of a cube of a side $x$ meters caused by increasing the side by $3$%.

Answer 1

$V=x^3$
$\frac{dv}{dx}=3x^2$
$\Delta v=3\%$ of

$=\frac{3}{100}\times x=\frac{3x}{100}$
W.K.T approximate change in volume
$\Delta v=\left(\frac{dv}{dx}\right)\Delta x$

$=3x^2\times \frac{3}{100}x$

$=\frac{9x^3}{100}$

$=0.09x^3$