= Solution
The stated <total differential> is that of $\pi r^2h$, so $V=\pi r^2h+C$. The zero-volume condition gives $C=0$. For positive $r,h$, divide the <total differential> by this <volume> to obtain
$$
\boxed{\frac{dV}{V}=2\frac{dr}{r}+\frac{dh}{h}.}
$$
For the specified small changes, $dV/V\approx2(0.01)+0.02=0.04$, so \b[the volume increases by approximately $4\%$]. The fractional expression requires $V>0$; at a degenerate zero-volume state it is undefined. For finite changes, the exact multiplier is $(1.01)^2(1.02)$, whose difference from $1$ is $4.0502\%$; the <total differential> gives its first-order approximation.
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