Question

CASE STUDY
In a toys manufacturing company, wooden parts are assemblet and painted to prepare a toy. Parte
wood processing activity center, the wood is taken out of storage to be sawed, after which trener
goes rough polishing, then is cut, drilled and has holes punched in it. It is then fine polished using
sandpaper. For the retail packaging and delivery activity center, the polished wood sub-mata
assembled together, then decorated using paint.
77mm
(110mm
72mm
40mm
One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is
and the height of its conical part is 77 mm. The diameters of the base of the comical part is numa
that of the cylindrical part is 40 mm,​

Answer 1

Given :-

• The total height of the toy = 110 mm .
• Height of its conical part = 77 mm .
• The diameters of the base of the conical part = 72 mm .
• The diameters of the base of the cylindrical part = 40 mm .

To Find :-

• Total painted surface area of conical part ?

Solution :-

we know that,

• Radius = Diameter / 2 .
• Slant height = √(radius² + height²)
• CSA of cone = π * radius * slant height .
• Base area of cone and cylinder = π * (radius)²

so,

→ Radius of conical part = 72/2 = 36 mm .

and,

→ Slant height of conical part = √(36² + 77²) = √(1296 + 5929) = √(7225) = 85 mm .

then,

→ CSA of conical part = (22/7) * 36 * 85 = (67320/7) = 9617.14 mm² .

now,

→ Radius of cylinder = 40/2 = 20 mm.

so,

→ Base area of cone to be painted = Base area of cone - Top base area of cylinder = π(36)² - π(20)² = π(36² - 20²) = (22/7) * 56 * 16 = 22 * 8 * 16 = 2816 mm².

therefore,

→ Total painted surface area of conical part = CSA of conical part + Base area to be painted = 9617.14 + 2816 = 12433.14 mm². (Ans.)

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Answer 2

Answer:

(i) Radius of cylindrical part, rcy = = 40

2 20 mm

Height of cylindrical part,

hcy = 110 − 77 = 33 mm

C.S.A. of cylinder 2 r h cy cy rcy

2 = p p +

= π r h cy ( ) 2 cy + rcy

= 20π ( ) 2 3 # 3 2 + 0

= 1720π mm2