The ratio between the radius of the base and the height of the cylinder is 2: 3.if its volume is 1617cm^3,the total surface area of the cylinder is?

The answer is 769.3 cm²

The volume of the cylinder is : V = π r² h
The ratio between the radius of the base and the height of the cylinder is 2:3:
r/h = 2/3
h = 3/2r

V = 1617 cm
π = 3.14

1617 = πr² * 3/2 r
1617 = πr³ * 3/2
1617 * 2/3 = πr³
1078 = πr³
r³ = 1078/π = 1078/3.14 = 343
r = ∛343 = 7 cm

h = 3/2r = 3/2 * 7 = 10.5 cm

The surface area of the cylinder is:
SA = 2πr² + 2πrh
      = 2 * 3.14 * 7² + 2 * 3.14 * 7 * 10.5
      = 307.72 + 461.58
      = 769.3 cm²