The sum of the radius of the base and height of a solid cylinder is 37 m.

Let $r$ and $h$ be the radius and height of the solid cylinder.

Given :

$r+h=37 \mathrm{~m}$

Total surface area, $S=2 \pi r(r+h)$

$1628=2 \pi \times r \times 37$

$\mathbf{r}=\frac{1628}{2 \pi \times 37}$

$=\frac{1628}{232.477}$

$=7 \mathrm{~m}$

Circumference of its base, $S_{1}=2 \pi \mathrm{r}$

$=\left(2 \times \frac{22}{7} \times 7\right) \mathrm{m}$

$=44 \mathrm{~m}$