Question
A water tank is in the shape of a right circular
cylinder of internal radius 7 m and height 14 m. It is closed at the top by a hemispherical dome of the same internal radius. The entire inner surface of the tank (including the dome and base) is to be painted with a waterproof coating at the rate of ₹15 per m². What is the total cost of painting the inner surface of the tank? (Take π = 22/7)Solution
Inner surfaces to be painted: – Curved surface of cylinder – Inner surface of hemispherical dome – Circular base of cylinder Radius r = 7 m, height h = 14 m Curved surface area of cylinder = 2πrh = 2 × (22/7) × 7 × 14 = 2 × 22 × 14 = 616 m² Inner surface area of hemisphere = 2πr² = 2 × (22/7) × 7² = 2 × (22/7) × 49 = 2 × 22 × 7 = 308 m² Base area of cylinder = πr² = (22/7) × 7² = (22/7) × 49 = 154 m² Total area = 616 + 308 + 154 = 1,078 m² Cost = 1,078 × 15 = ₹16,170
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