Question

If there is an error of k% in measuring the edge of a cube, then the percent error in estimating its volume is

• A. $k$
• B. $3k$
• C. $\frac{k}{3}$
• D. None of these

Answer 1

Answer: (B)

$3k$

Volume V of a cube of side x is given by $V=x^3$
$\Rightarrow \frac{dV}{dx}=3x^2$
Let the change in x be $\Delta x=K$% of $x=\frac{kx}{100}$
Now, the change in volume,
$\Delta V=\left(\frac{dV}{dx}\right)\Delta x=3x^2\left(\Delta x\right)$
$=3x^2\left(\frac{kx}{100}\right)=\frac{3x^3.k}{100}$
$\therefore$ Approximate change in volume
$=\frac{3k{x}^3}{100}=\frac{3k}{100}.x^3$
$=3k$ % of original volume