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10 A semi-circular sheet of metal of diameter 28 cm is bent into an open conical cup. Determine thdepth and capacity of the cup. |
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Answer» Slant height of the conical cup, 'l' = radius of the semi-circular sheet, R = 14 cmLet radius and height of the conical cup be 'r' and 'h' respectively.Circumference of the base of the cone = Length of arc of the semi-circleOr, 2πr = (1/2)2πROr, 2πr = (1/2)(2π)(14)Or, r = 7 cmNow, we know that l² = h² + r²(14)² = (h)² + (7)²h² = 196 - 49h =√147Height or depth of the conical cup = 12.124 cmNow, capacity of the conical cup = 1/3πr²h= 1/3*22/7*7*7*12.124= 13069.672/21Capacity of the conical cup = 622.365 cu cm |
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