GATE 2020 AG – Question 57
Pond contour elevations 100, 101, 102, 103, 104, 105 and 106 m enclose areas 440, 580, 640, 740, 960, 1100 and 1240 m², respectively. Estimate capacity in m³ by the trapezoidal rule.
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Correct answer: 4860 to 4860
Explanation
Contour spacing is 1 m. The two endpoint half-areas sum to (440+1240)/2 = 840 m². The five interior areas sum to 4020 m². Multiply their combined contribution by the spacing: V = 1 × (840+4020) = 4860 m³. Endpoint areas receive half weight; every interior contour receives full weight.