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(C) The volume $V$ of a cube with side $x$ is given by $V = x^{3}$.The approximate change in volume $dV$ is given by the formula $dV = \left(\frac{dV}

Vedclass · Accepted Answer

$0.03 \,x^{3} \, m^{3}$

Vedclass · Answer

(C) The volume $V$ of a cube with side $x$ is given by $V = x^{3}$.The approximate change in volume $dV$ is given by the formula $dV = \left(\frac{dV}{dx}ight) \Delta x$.First,differentiate $V$ with respect to $x$:$\frac{dV}{dx} = 3x^{2}$.Given that the side $x$ increases by $1 \%$,the change in side $\Delta x$ is $1 \% 	ext{ of } x = 0.01x$.Now,substitute these values into the formula for $dV$:$dV = (3x^{2}) 	imes (0.01x)$.$dV = 0.03x^{3}$.Therefore,the approximate change in the volume of the cube is $0.03 \,x^{3} \, m^{3}$.

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

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