Solution;

(i) Given height of the rocket = 26 cm

Height of the cone, H = 6 cm

Height of the cylinder, h = 26-6 = 20 cm

Diameter of the cone = 5 cm

Radius of the cone, R = 5/2 = 2.5 cm

Diameter of the cylinder = 3 cm

Radius of the cylinder, r = 3/2 = 1.5 cm

Slant height of cone, , l = √(H²+r²)

l = √(6²+2.5²)

l = √(36+6.25)

l = √(42.25)

l = 6.5 cm

Curved surface area of the cone = Rl

= 3.14×2.5×6.5

= 51.025 cm²

Base area of cone = R²

= 3.14×2.5²

= 3.14×6.25

= 19.625 cm²

Curved surface area of the cylinder = 2rh

= 2×3.14×1.5×20

= 188.4 cm²

Base area of cylinder = r²

= 3.14×1.5²

= 3.14×2.25

= 7.065 cm²

Total surface area of conical portion to be painted green = Curved surface area of the cone+ Base area of cone- Base area of cylinder

= 51.025 + 19.625 – 7.065

= 63.585 cm²

= 63.59 cm²

Hence the area of the rocket painted with green colour is 63.59 cm².

Total surface area of the cylindrical portion to be painted red = Curved surface area of the cylinder + Base area of cylinder

= 188.4+7.065

= 195.465 cm²

= 195.47 cm²

Hence the area of the rocket painted with red colour is 195.47 cm².

(ii) Volume of wood in the rocket = Volume of cone + Volume of cylinder

= (1/3)R²H + r²h

= ((R²H/3) + r²h))

= 3.14×((2.5²×6/3) + 1.5²×20)

= 3.14×((6.25×2) + 2.25×20)

= 3.14×(12.5+ 45)

= 3.14×57.5

= 180.55 cm³

Hence the volume of the wood in the rocket is 180.55 cm³.