Approximate change in the volume $V$ of a cube of side $x$ metres caused by increasing the side by 3% is

0.09 x^{3} m^{3}

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0.03 x^{3} m^{3}

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0.06 x^{3} m^{3}

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0.04 x^{3} m^{3}

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Solution

The correct option is A $0.09 x^{3} m^{3}$
Volume, $V = x^{3}$
Change in volume, $d V = \frac{d V}{d x} Δ x$
$\Rightarrow d V = 3 x^{2} Δ x$
$\Rightarrow d V = 3 x^{2} \times 0.03 x [Given Δ x = 3 %]$

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