the internal and external diameters of a hollow hemispherical vessel are 24cm and 25cm,respectively. If the cost of painting 1cm² of the surface area is Rs0.05,then find the total cost of painting the vessel all over.
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Inner diameter = 24 cm , inner radius = 12 cm
Outer dia = 25 cm. , outer radius = 12.5 cm
Thickness = 0.5 cm
Inner curved surface area = 2 π 12² cm² (hemispherical)
Outer curved surface area = 2 π 12.5² cm²
Flat surface area of base ring = π (12.5² - 12²) cm²
Adding the three surfaces =TSA = π (12² + 3*12.5²) = 1925 cm²
Cost = 1, 925 * 0.05 = Rs 96.25
Outer dia = 25 cm. , outer radius = 12.5 cm
Thickness = 0.5 cm
Inner curved surface area = 2 π 12² cm² (hemispherical)
Outer curved surface area = 2 π 12.5² cm²
Flat surface area of base ring = π (12.5² - 12²) cm²
Adding the three surfaces =TSA = π (12² + 3*12.5²) = 1925 cm²
Cost = 1, 925 * 0.05 = Rs 96.25
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Answered by
1
Answer:
96.28 rupees
Step-by-step explanation:
let the external and internal radii of the hemispherical vessel be R and r respectively
Then
R= 12.5cm
r= 12cm
area of outer surface=2πR²
area of inner surface=2πr²
area of the ring at the top=πR²-πr²
Total area to be painted= (2πR²+2πr²+πR²-πr²)
Total area to be painted=π(3R²+r²)
Total area to be painted=22/7×{3×(12.5)²+(12)²}
Total area to be painted=22/7×{3×(25/2)²+(12)²}
Total area to be painted=22/7×{468.75+144}
Total area to be painted=22/7×612.75 cm²
=13480.5/7
=1925.78 cm²
Cost of painting
=(1925.78×0.05) rupees
=96.28 rupees
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