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Deepak Bora
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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 colors.

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This problem is the combination of two shape that is cone and cylinder. In the given problem use π = 22/7. This problem from RS Aggarwal book problem number 32, page number 289, exercise 17A, chapter volume and surface area of solid.

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  1. We have,

    the base radius of the conical part, r =5/2 =  2. 5 cm,

    the base radius of the cylindrical part, R = 4/2 = 2 cm,

    the total height of the toy = 26 cm,

    the height of the conical part, h = 6 cm

    Also, the height of the cylindrical part H = 26-6 = 20cm

    slant height of the conical part, l

    By using pathogroups theorem

    l = √(r² + h²)

    l = √([2.5]² + [6]²)

    ∴ l = 6.5 cm

    Now,

    Area painted by red color = curved surface area of cone + area of base of conical part – area of base of cylindrical  part

    = πrl + πr² – πR²

    = π [ rl + r² – R² ]

    = 22/7 ( [2.5*6.5] + [2.5]² – 2² )

    = 58.14 cm²

    Now,

    Area painted by white color = curved surface area of cylinder + area of base of cylindrical  part

    = 2πRH + πR²

    = πR [2H + R]

    = [22/7] [2] ( 2 *20 + 2 )

    = 264 cm²

    ∴ Area painted by red color is 58.14 cm²

    ∴ Area painted by white color is 264 cm²

     

     

     

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