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

Example 3 - Chapter 13 Class 10 Surface Areas and Volumes - Part 2
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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 π= 3.14) 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 the cone Curved Surface area of cone = 𝜋𝑟𝑙 Diameter of conical portion = 5 cm Radius of conical portion = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 5/2 = 2.5 cm Height of the conical part = h = 6 cm We need to find 𝑙 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 = √(169/4) l = √(〖13〗^2/2^2 ) l = 13/2 l = 6.5 cm Curved Surface area of cone = 𝜋𝑟𝑙 = 3.14 ×2.5×6.5 = 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 = 𝜋𝑟2 = 3.14 × (2.5)2 = 3.14×6.25 = 19.625 cm2 Curved Surface area of the cylinder Diameter of cylinder = 3 Radius of cylinder = r = 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟/2 = 3/2 = 1.5 cm Height of cylinder = Total height – Height of cone = 26 – 6 = 20 cm Curved Surface area of the cylinder = 2𝜋𝑟h = 2 ×3.14×1.5×20 = 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 = 𝜋𝑟2 = 3.14 × (1.5)2 = 7.065 cm2 Hence, 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 = 70.65 – 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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.