The approximate change in the volume of a cub | vedclass

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

Vedclass · Accepted Answer

$0.09$

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(A) The volume of a cube $(V)$ 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 increases by $3 \%$,the change in side $\Delta x = 3 \% 	ext{ of } x = 0.03x$.Now,substitute these values into the formula for $dV$:$dV = (3x^{2}) 	imes (0.03x)$$dV = 0.09x^{3} 	ext{ m}^{3}$.Thus,the approximate change in the volume of the cube is $0.09x^{3} 	ext{ m}^{3}$.

The approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3 \%$ is (in $x^{3} \text{ m}^{3}$)

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