Question

The approximate change in volume $V$ of a cube of side $x$ meters caused by increasing the side by $2$% is:

• A. $0.03x^3$ cubic meter
• B. $0.04x^3$ cubic meter
• C. $0.06x^3$ cubic meter
• D. $0.08x^3$ cubic meter

Answer 1

The correct option is C $0.06x^3$ cubic meter

We have volume $V=x^3$
$\Rightarrow dV=\left(\frac{dV}{dx}\right)△x$
$=\left(3x^2\right)△x$
$=\left(3x^2\right)\left(0.02x\right)$
$=0.06x^3{m}^3$
Thus the approximate change in volume $V$ is $0.06x^3{m}^3$