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.