Question

In a wooden toy manufacturing industry a toy is prepared. The toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 14 cm and the height of it's comical part 4cm.The diameter of the base of the conical part is 6cm and that of the cylindrical part is 4 cm
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Answer 1

Complete Question :- In a wooden toy manufacturing industry a toy is prepared. The toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 14 cm and the height of it's conical part 4cm. The diameter of the base of the conical part is 6cm 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.

Solution :-

from given data we have,

• Radius of conical part = r = Diameter / 2 = 6/2 = 3 cm.
• Radius of cylindrical part = R = Diameter / 2 = 4/2 = 2 cm .
• Height of conical part = 4 cm .
• Height of cylindrical part = H = 14 - 4 = 10 cm.
• Slant height of conical part = l = √(radius² + height²) = √(3² + 4²) = √(9 + 16) = √(25) = 5 cm.

so,

→ The area to be painted red = CSA of cone + Conical Base - Cylindrical base .

→ Red painted area = πrl + πr² - πR²

→ Red painted area = π(rl + r² - R²)

→ Red painted area = π(3*5 + 3² - 2²)

→ Red painted area = π(15 + 9 - 4)

→ Red painted area = 3.14 * 20

→ Red painted area = 62.8 cm² (Ans.)

and,

→ The area to be painted white = CSA of cylinder + Cylindrical base .

→ White painted area = 2πRH + πR²

→ White painted area = πR(2H + R)

→ White painted area = π * 2(2 * 10 + 2)

→ White painted area = 2π(20 + 2)

→ White painted area = 2π * 22

→ White painted area = 44π

→ White painted area = 44 * 3.14

→ White painted area = 138.16 cm² (Ans.)

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