Newbie

# 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.

• 0

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.

Share

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 + 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 *20 + 2 )

= 264 cm²

∴ Area painted by red color is 58.14 cm²

∴ Area painted by white color is 264 cm²

• 1