Example 3 - A wooden toy rocket is in shape of a cone - Surface Area - Added

  1. Chapter 13 Class 10 Surface Areas and Volumes
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Example 3 A wooden toy rocket is in the shape of a cone mounted on a cylinder, as shown in figure. The height of the entire rocket is 26 cm, while the height of the conical part is 6 cm. The base of the conical portion has a diameter of 5 cm, while the base diameter of the cylindrical portion is 3 cm. If the conical portion is to be painted orange and the cylindrical portion yellow, find the area of the rocket painted with each of these colours. (Take ฯ€= 3.14) Area to be painted orange = Curved surface area of the cone + Base area of the cone โ€“ 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 the cone Curved Surface area of cone = ๐œ‹๐‘Ÿ๐‘™ Diameter of conical portion = 5 cm Radius of conical portion = r = ๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ/2 = 5/2 = 2.5 cm Height of the conical part = h = 6 cm We need to find ๐‘™ first We know that l2 = h2 + r2 l2 = (6)2 + (5/2)^2 l2 = 36 + 25/4 l2 = (36(4) + 25)/4 l2 = 169/4 l = โˆš(169/4) l = โˆš(ใ€–13ใ€—^2/2^2 ) l = 13/2 l = 6.5 cm Curved Surface area of cone = ๐œ‹๐‘Ÿ๐‘™ = 3.14 ร—2.5ร—6.5 = 51.025 cm2 Base area of the cone Base of cone is a circle with radius = radius of cone = 2.5cm Base area of cone = Area of circle = ๐œ‹๐‘Ÿ2 = 3.14 ร— (2.5)2 = 3.14ร—6.25 = 19.625 cm2 Curved Surface area of the cylinder Diameter of cylinder = 3 Radius of cylinder = r = ๐ท๐‘–๐‘Ž๐‘š๐‘’๐‘ก๐‘’๐‘Ÿ/2 = 3/2 = 1.5 cm Height of cylinder = Total height โ€“ Height of cone = 26 โ€“ 6 = 20 cm Curved Surface area of the cylinder = 2๐œ‹๐‘Ÿh = 2 ร—3.14ร—1.5ร—20 = 188.4 cm2 Base area of the cylinder Base of cone is a circle with radius = radius of cylinder = 1.5 cm Base area of cylinder = Area of circle = ๐œ‹๐‘Ÿ2 = 3.14 ร— (1.5)2 = 7.065 cm2 Hence, Area to be painted orange = Curved surface area of the cone + Base area of the cone โ€“ Base area of the cylinder = 51.025 + 19.625 โ€“ 7.0625 = 70.65 โ€“ 7.0625 = 63.58 cm2 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 cm2 Hence, area to be painted yellow = 195.465 cm2

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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