Question

The approximate change in volume $V$ of a cube of sides $x$ meters caused by increasing the side by $1\%$ is

• A. $0.01x^3{m}^3$
• B. $0.09x^3{m}^3$
• C. $0.06x^3{m}^3$
• D. $0.03x^3{m}^3$

Answer 1

The correct option is D $0.03x^3{m}^3$

Volume of the cube,
$V=x^3\Rightarrow \frac{dV}{dx}=3x^2$
$\Delta V=\frac{dV}{dx}\times \Delta x=3x^2\times \Delta x$
We know that $\Delta x=\frac{1}{100}\times x=0.01x$
$\therefore \Delta V=3x^2\times 0.01x=0.03x^3{m}^3$