The internal and external diameters of a hollow hemispherical vessel are 21 cm and 25.2 cm respectively. The cost of painting 1 cm² of the surface is 10 paise. Find the total cost to paint the vessel all over.
Answers
Given,
internal diameter=21cm
internal radius=21/2=10.5cm
external diameter=25.2cm
external radius=25.2/2 =12.6cm
surface area of internal bowl=2πr²
=2(22/7)(10.5²)
=2×22×10.5×10.5/7
=693cm²
surface area of external bowl=2πR²
=2(22/7)(12.6²)
=2×22×12.6×12.6/7
=997.9cm²
surface area of ring=π(R²-r²)
=22/7(12.6²-10.5²)
=22/7(48.51)
=22×48.51/7
=152.46cm²
cost of internal bowl=693×0.1=69.3
cost of external bowl=997.9×0.1=99.79
cost of ring=152.46×0.1=15.246
cost of bowl=69.3+99.7+15.2=184.2
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Answer:
The total cost to paint the vessel all over is ₹ 184.34.
Step-by-step explanation:
Given :
Internal diameter of the hollow hemispherical vessel = 21 cm
Internal radius of the hollow hemispherical vessel , r = 21/2 = 10.5 cm
External diameter of the hollow hemispherical vessel = 25.2 cm
External radius of the hollow hemispherical vessel , R = 25.2/2 =12.6 cm
Total area of the hollow hemispherical vessel to paint = Curved surface area of outer hemisphere + Curved surface area of inner hemisphere + area of base of hollow hemisphere
= 2πR² + 2πr² + π(R²− r²)
= 2π(R² + r²) + π(R²− r²)
= π [2(R² + r²) + (R²− r²)]
= π [2(12.6)² + (10.5)² + (12.6² −10.5²)
= π[2 × (158.76 + 110.25) + (158.76 - 110.25
= π [2 × 269.01 + 48.51]
= π [ 538.02 + 48.51]
= π × 586.53
= 22/7 × 586.53
= 83.79 × 22
Total area of the hollow hemispherical vessel to paint = 1843.38 cm²
Given : The cost of painting of 1 cm ² of the surface is = 10 p = 10/100 = ₹ 0.1 [1 p = 1/100 ₹]
Total cost of painting = 1848.38 × 0.10 = ₹ 184.34
Hence, The total cost of painting all over the vessel is ₹ 184.34
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