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 the conical part is 72 mm and that of the cylindrical part is 40 mm.
(v) If the toy manufacturer company charge 3 paise for 32 pi mm3 of wood, what is the price of a box of 100 toys?
Answers
Given : 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 the conical part is 72 mm and that of the cylindrical part is 40 mm.
conical part is to be painted blue
To Find : surface area need to be painted is
Solution:
Diameter of conical part = 72 mm
=> radius of conical part = 72/2 = 36 mm
Height of conical part = 77 mm
Slant height of conical part = √36² + 77²
= 85 mm
Curved Surface area of cone = πrL
= (22/7)* 36 * 85
= 9,617.14 mm²
Base area of cone to be painted = base area of cone - top area of cylinder
radius of top of cylinder = 40/2 = 20 mm
Base area of cone to be painted = π (36² - 20²)
= (22/7)(56)(16)
= 2816 mm²
Total area to be painted = 9,617.14 + 2816
= 12,433.14 mm²
height of cylinder = 110 - 77 = 33 mm
Volume = (1/3)π36²(77) + π(20)²* 33
= 33,264π + 13,200π
= 46,464π mm³
32π cost 3 paise
=> 3200π cost Rs 3
=> 46,464π cost = 46464 * 3 / 3200 = 4356/100 Rs
Cost of 100 boxes = 4356 Rs
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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: