A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. [Take t = 22/7.]
Answers
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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
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