Subtopic: Measurement of infiltration, soil moisture and irrigation water infiltration
Question Statement:
The areas within the contour lines at the site of a proposed reservoir and dam are as follows:
| Contour (m) | 20 | 22 | 24 | 26 | 28 | 30 | 32 |
|---|---|---|---|---|---|---|---|
| Area (m²) | 100 | 220 | 600 | 1800 | 4500 | 10000 | 25000 |
If 20 m R.L. represents the bottom of the reservoir and 32 m R.L. represents the water surface, the volume of water in the reservoir obtained by the trapezoidal formula is:
Options:
(A) 21110 m³
(B) 32220 m³
(C) 42220 m³
(D) 59340 m³
Official Answer Key:
D
Step-by-Step Solution & Explanation
Trapezoidal formula: V = (h/2)·Σ(A_i + A_{i+1}) over successive contour intervals, h=2 m. V = (2/2)[(100+220)+(220+600)+(600+1800)+(1800+4500)+(4500+10000)+(10000+25000)] = 320+820+2400+6300+14500+35000 = 59,340 m³.
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