Answer
$ a.\quad$ acceptable.
$ b.\quad$not acceptable.
Work Step by Step
a.
Does $x=2.999$ satisfy
$|x-3|\leq 0.01\quad ?$
$|2.999-3.000|=|-0.001|=0.001.$
Since $0.001\leq 0.010$, the radius $2.999$ is acceptable.
b.
Does $x=2.89$ satisfy
$|x-3|\leq 0.01\quad ?$
$|2.89-3.00|=|-0.11|=0.11.$
Since $0.11\gt 0.01$, the radius $2.89$ is not acceptable
