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(A) The volume 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}

Vedclass · Accepted Answer

$0.06 \, x^{3} \, m^{3}$

Vedclass · Answer

(A) The volume 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 $x$ is increased by $2 \%$,the change in side $\Delta x = 2 \% 	ext{ of } x = 0.02x$.Now,substitute these values into the formula for $dV$:$dV = (3x^{2}) 	imes (0.02x) = 0.06x^{3} \, m^{3}$.Thus,the approximate change in volume is $0.06x^{3} \, m^{3}$.

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2 \%$.

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