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(B) The surface area $S$ of a cube with side $x$ is given by $S = 6x^{2}.$To find the approximate change in surface area $(\Delta S)$,we use the diffe

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$0.12 \,x^{2} \,m^{2}$

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(B) The surface area $S$ of a cube with side $x$ is given by $S = 6x^{2}.$To find the approximate change in surface area $(\Delta S)$,we use the differential formula $\Delta S \approx \frac{dS}{dx} \cdot \Delta x.$First,differentiate $S$ with respect to $x$:$\frac{dS}{dx} = \frac{d}{dx}(6x^{2}) = 12x.$The side is decreased by $1\%$,so the change in side $\Delta x = -0.01x.$Now,calculate the approximate change:$\Delta S \approx (12x) \cdot (-0.01x) = -0.12x^{2}.$The magnitude of the approximate change in the surface area is $0.12x^{2} \, m^{2}.$

Find the approximate change in the surface area of a cube of side $x$ metres caused by decreasing the side by $1 \%.$

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