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

Solution:

Given data is as follows:

h + r = 37 cm

Total surface area of the cylinder $=1628 \mathrm{~cm}^{2}$

That is,

$2 \pi r h+2 \pi r^{2}=1628$

2πr(h + 2r) = 1628

But it is already given in the problem that,

h + r = 37 cm

Therefore, 2πr × 37 = 1628

2 × 22/7 × r × 37 = 1628

r = 7 cm

Since, h + r = 37 cm

We have, h + 7 = 37 cm

H = 30 cm

Now that we know both height and radius of the cylinder, we can easily find the volume.

Volume $=\pi r^{2} h$

Volume = 22/7 × 7 × 7 × 30

Hence, the volume of the given cylinder is $4620 \mathrm{~cm}^{3}$.