Question

Find the approximate changes in the volume 'V' of a cube of side x metres caused by decreasing the side by $1\%$.

Answer 1

Volume$=V$

Side of the cube=$x$ metres

decrease in side$=1\%$

$=0.01\times x$

$=0.01x$

Volume of a cube $=l\times b\times h$

$=x\times x\times x$

$=x^3$

Approximate change in volume $=\Delta V$

$=\frac{dv}{dx}\times \Delta x$

$V=x^3$

$\frac{dv}{dx}=3x^2=[$Differentiating with respect to $x]$

$\Delta V=\frac{dv}{dx}\times \Delta x$

$=3x^2\times 0.01x$

$=0.03x^3{m}^3$