The ratio between the radius of the base and the height of a cylinder is 2 : 3.

Let r cm be the radius and h cm be the height of the cylinder. It is given that the ratio of r and h is 2:3, so h = 1.5r
The volume of the cylinder (V) is 1617 cm3.

So, we can find the radius and the height of the cylinder from the equation given below:

V= πr2h

1617 = πr2h

1617 = πr2(1.5r)

 r3 =343

r = 7 cm and h = 10.5 cm

Total surface area = 2πr2+2πrh

$=2 \times \frac{22}{7} \times 7^{2}+2 \times \frac{22}{7} \times 7 \times 10.5=770 \mathrm{~cm}^{2}$

Hence, the total surface area of the cylinder is 770 cm2.