Question

A quantity $z$, to be estimated has a dependency on the variables $a, b$ and $c$ as $z=a b^{2} c^{-2}$. The percentage of error in the measurement of $a, b$ and $c$ are respectively, $2.1 \%, 1.3 \%$ and $2.2 \%$. The percentage of error in the measurement of $z$ would then be

• A. $5.6 \%$
• B. $1.6 \%$
• C. $1.0 \%$
• D. $9.1 \%$

Answer 1

Answer: (D)

$9.1 \%$

Answer 2

Given , $z =a b^{2} c^{-2}$
So, the percentage error in the volume is given by
$\frac{\Delta z}{z} \times 100=\left[\frac{\Delta a}{a}+2 \frac{\Delta b}{b}+2 \frac{\Delta c}{c}\right] \times 100$
$=2.1 \%+2(1.3 \%)+2(2.2 \%)=9.1 \%$