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