Question
Find the cost of painting all surfaces of a 10 m long
hollow steel pipe whose internal and external diameters measure 15 cm and 17 cm respectively, if the cost of painting 1 cm² of the surface is ₹0.15. [Use π = 22/7]Solution
External diameter = 17 cm Internal diameter = 15 cm Cost of painting = Rs 0.15 per cm² Height of cylinder = 10 m = 1000 cm External Radius(R) = 17/ 2 = 8.5 cm Internal Radius(r) = 15/ 2 = 7.5 cm Total Surface Area of a hollow cylinder = 2πh (R + r) + 2π (R² - r²) Total Surface area = 2π × 1000 × (8.5 + 7.5) + 2π [ (8.5) ² - (7.5) ²] 2π [1000×16+16] 2π×16[1000+1) 2×22/7×1001 = 100672 cm² Total cost of painting the cylinder = 100672 x 0.15 Rs 15100.80
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