Question

Find the approximate change in the value V of a cube of side x metres caused by increasing the side by 1%

Answer 1

volume$=V$

side of the cube $=x$ m

increase 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 $\Delta V$

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

$V=x^3$

$\frac{dv}{dx}3x^2\left[Differentiatingwithrespecttox\right]$

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

$=3x^2\times 0.01x$

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