Find the approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3$ %.

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Solution

Change in volume $Δ V = \frac{d V}{d x} Δ x$ , the volume of cube of side $x m$ is $x^{3} m^{3}$ .
The change in $x$ $Δ x = 0.03 x m$
Change in volume $Δ V = 3 x^{2} \times 0.03 x = 0.09 x^{3} m^{3}$

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Find the approximate change in the volume of a cube of side x metres caused by increasing the side by 3%.

Change in volume ΔV=dVdxΔx , the volume of cube of side xm is x3m3. The change in x Δx=0.03xmChange in volume ΔV=3x2×0.03x=0.09x3m3

Find the approximate change in the volume of a cube of side $x$ metres caused by increasing the side by $3$ %.

Change in volume $Δ V = \frac{d V}{d x} Δ x$ , the volume of cube of side $x m$ is $x^{3} m^{3}$ .
The change in $x$ $Δ x = 0.03 x m$
Change in volume $Δ V = 3 x^{2} \times 0.03 x = 0.09 x^{3} m^{3}$