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A well 20 m in diameter is dug 14 m deep and the earth taken out is spread all around it to a width of 5 m to form an embankment. The height of the embankment is :
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- 10 m
- 11 m
- 11.2 m
- 11.5 m
- 10 m
Correct Option: C
| Radius of the base of well = | = 10 m | |
| 2 |
| Volume of the earth taken out = πr²h = | × 10² × 14 m³ | |
| 7 |
Let the height of embankment be x metres. Then,
Volume = π (R² – r²) × x, where R = 15 m, r = 10m
| Volume = | (15² – 10²) × x | |
| 7 |
| = | × 25 × 5 × x | |
| 7 |
Clearly,
| = | × 25 × 5 × x | |
| 7 |
| = | 10² × 14 | |
| 7 |
| ⇒ x = | = 11.2 m | |
| 25 × 5 |
