Answer
$3 r \%$
Work Step by Step
We know the equation:
\[
l w h=V
\]
Obtaining the total derivative of volume $\mathrm{V}$ i.e $d V$
\[
l h d w+l w d h+w h d l=d V
\]
\[
\frac{d l}{l}+\frac{d w}{w}+\frac{d h}{h}=\frac{d V}{V}
\]
We can write
\[
\begin{array}{|c|c|c|}
\frac{d V}{V}|=| \frac{d l}{l}+\frac{d w}{w}+\frac{d h}{h} | \\
\frac{d V}{V}|\leq| \frac{d l}{l}|+| \frac{d w}{w}|+| \frac{d h}{h} | &
\end{array}
\]
We are given that
\[
\begin{aligned}
\frac{d l}{l}|=| \frac{d w}{w} &=\left|\frac{d h}{h}\right|=\frac{r}{100} \\
\frac{d V}{V} | & \leq \frac{3 r}{100}
\end{aligned}
\]
Therefore, the maximum percentage error in measured $V$ is $3 r \%$
