Question:
The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is
A. $0.06 x^{3} \mathrm{~m}^{3}$
B. $0.6 x^{3} \mathrm{~m}^{3}$
C. $0.09 x^{3} \mathrm{~m}^{3}$
D. $0.9 x^{3} \mathrm{~m}^{3}$
Solution:
The volume of a cube $(V)$ of side $x$ is given by $V=x^{3}$.
$\therefore d V=\left(\frac{d V}{d x}\right) \Delta x$
$=\left(3 x^{2}\right) \Delta x$
$=\left(3 x^{2}\right)(0.03 x) \quad[$ As $3 \%$ of $x$ is $0.03 x]$
$=0.09 x^{3} \mathrm{~m}^{3}$
Hence, the approximate change in the volume of the cube is $0.09 x^{3} \mathrm{~m}^{3}$.
The correct answer is $\mathrm{C}$.