A toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 51 mm and the height of its conical part is 18 mm. The diameters of the base of the conical part is 48 mm and that of the cylindrical part is 40 mm.
If curved surface of the cylindrical part is to be painted red, the surface area needs to be painted is
Answers
Step-by-step explanation:
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
Curved surface area of cone =πrl
l=
6
2
+2.5
2
l=
36+6.25
l=
42.25
l=6.5 cm
Curved surface area of cone =3.14×2.5×6.5
=51.025 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(2.5)
2
=3.14×6.25
=19.625 cm
2
Curved surface area of cylinder =2πrh
=2×3.14×1.5×20
=188.4 cm
2
Base area of cone = Area of circle
=πr
2
=3.14×(1.5)
2
=7.065 cm
2
Area to be painted orange = Curved surface area of the cone + Base area of the cone − Base area of the cylinder
=51.025+19.625−7.0625
=63.59 cm
2
Area to be painted yellow = Curved surface area of the cylinder + Area of one bottom base of the cylinder
=188.4+7.065
=195.465 cm
2
Hence,
Area to be painted orange =63.59 cm
2
Area to be painted yellow =195.465 cm
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: