Example-9. A wooden toy rocket is in the shape of a cone mounted on a cylinder as shown in the adjacent figure. The height of the entire rocket is 26 cm, while the height of the conical partis 6cm. The base of the conical position has a diameter of 5cm, while the base diameter of the cylindrical portion is 3cm. If the conical portion is to be painted orange and the cylindrical portion is to be painted yellow, find the area of the rocket painted with each of these colour (Take a = 3.14)
Answers
Answer:
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
Curved surface area of cone =πrl
l=
6
2
+2.5
2
l=
36+6.25
l=
42.25
l=6.5 cm
Curved surface area of cone =3.14×2.5×6.5
=51.025 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(2.5)
2
=3.14×6.25
=19.625 cm
2
Curved surface area of cylinder =2πrh
=2×3.14×1.5×20
=188.4 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(1.5)
2
=7.065 cm
2
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
=51.025+19.625−7.0625
=63.59 cm
2
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
=188.4+7.065
=195.465 cm
2
Hence,
Area to be painted orange =63.59 cm
2
Area to be painted yellow =195.465 cm
2
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
Curved surface area of cone =πrl
l=
6
2
+2.5
2
l=
36+6.25
l=
42.25
l=6.5 cm
Curved surface area of cone =3.14×2.5×6.5
=51.025 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(2.5)
2
=3.14×6.25
=19.625 cm
2
Curved surface area of cylinder =2πrh
=2×3.14×1.5×20
=188.4 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(1.5)
2
=7.065 cm
2
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
=51.025+19.625−7.0625
=63.59 cm
2
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
=188.4+7.065
=195.465 cm
2
Hence,
Area to be painted orange =63.59 cm
2
Area to be painted yellow =195.465 cm
2