Question

In a toys manufacturing company, wooden parts are assembled and painted to prepare a toy. One specific toy is
in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical
part is 77 mm. The diameters of the base of conical part is 72mm and that of the cylindrical part is 40 mm.

Answer 1

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Answer 2

Answer:

Given :-

Total height of the toy = 110mm .

Height of conical part = 77mm.

Diameter of base of conical part = 72mm.

Diameter of cylindrical part = 40mm.

Cost of painting the toy = 2 paise for 8π mm²

To Find :-

The cost of painting of a box of 100 toys .

Solution :-

we know that,

Radius = Diameter / 2 .

CSA of cone = π * radius * slant height.

Slant height = √[length² + radius²]

CSA of cylinder = 2 * π * radius * height .

so,

→ Height of conical part = 77mm.

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

then,

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

so,

→ CSA of conical part = π * 36 * 85 = 3060π mm².

also,

→ Base Area of conical part = Base Area of conical part - Base Area of Top of cylinder = π(36)² - π(20)² = π(36² - 20²) = π(36 + 20)(36 - 20) = π * 56 * 16 = 896π mm².

then,

→ Total area to be painted of conical part = 3060π + 896π = 3956π mm².

also,

→ Cylindrical area painted = 2 * π * 20 * 33 + π * (20)² = 1320 π + 400π = 1720 mm².

therefore,

→ Total painted area = 3956π + 1720π = 5676π mm² .

hence,

→ 8π mm² costs = 2 paise

→ π mm² costs = (2/8π) paise

→ 5676π mm² costs = (2/8π) * 5676π = 1419 paise.

∴

→ Cost of painting of a box of 100 toys = 1419 * 100 = 141900 paise = (141900/100) = Rs.1419 (Ans.) (Option C)

Step-by-step explanation: