#### Answer

$a). 3 $
$b). 246\,cm^{2}$

#### Work Step by Step

a). Among the inputs 12.559 cm and 5.62 cm, minimum number of significant figures is 3. So, final area should also have 3 significant figures.
b). Outside area = Curved surface area + Base areas.
$ = 2 \times\frac{22}{7} \times r \times h + 2 \times \frac{22}{7} \times r^{2}$
where, $r=\frac{12.559}{2} cm, h=5.62 cm$
So, area $=246 \,cm^{2}$