A new 200-metre long dam is to be built.
The plan for the new dam shows evenly spaced cross-sectional areas.
- Using the Trapezoidal rule, show that the volume of the dam is approximately 44 500 m³. (2 marks)
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- It is known that the catchment area for this dam is 2 km².
Assuming no wastage, calculate how much rainfall is needed, to the nearest mm, to fill the dam. (2 marks)
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Show Worked Solution
| i. |  |
| `V` | `~~ 50/2[360 + 2(300 + 270 + 140) + 0]` |
| `~~ 25(1780)` | |
| `~~ 44\ 500\ text(m³)` |
ii. `text(Convert 2 km² → m²:)`
♦♦♦ Mean mark 11%.
| `text(2 km²)` | `= 2000\ text(m × 1000 m)` |
| `= 2\ 000\ 000\ text(m²)` |
`text(Using)\ \ V=Ah\ \ text(where)\ \ h= text(rainfall):`
| `44\ 500` | `= 2\ 000\ 000 xx h` |
| `:.h` | `= (44\ 500)/(2\ 000\ 000)` |
| `= 0.02225…\ text(m)` | |
| `= 22.25…\ text(mm)` | |
| `= 22\ text{mm (nearest mm)}` |
