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.

Deepak BoraNewbie

# 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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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