Solution;

Given diameter of the cylinder = 6 cm

Radius of the cylinder, r = 6/2 = 3 cm

Height of the cylinder, H = 12 cm

Slant height of the cone, l = 5 cm

Radius of the cone, r = 3 cm

Height of the cone, h = √(l²-r²)

h = √(5²-3²)

h = √(25-9)

h = √16

h = 4 cm

Total surface area of the rocket = curved surface area of cylinder +base area of cylinder+ curved surface area of cone

= 2rH+r²+rl

= r(2H+r+l)

= 3.14×3×(2×12+3+5)

= 3.14×3×(24+3+5)

= 3.14×3×32

= 301.44 cm²

Hence the Total surface area of the rocket is 301.44 cm².

Volume of the rocket = Volume of the cone + volume of the cylinder

= (1/3)r²h +r²H

= r²((h/3)+H)

= 3.14×3²×((4/3)+12)

= 3.14×9×((4+36)/3)

= 3.14×9×(40/3)

= 3.14×3×40

= 376.8 cm³

Hence the volume of the rocket is 376.8 cm³.