A) 10 m
B) 11 m
C) 11.2 m
D) 11.5 m
Correct Answer: C
Solution :
| Radius of base of well \[=\frac{20}{2}=10\,\,\text{m}\] |
| Volume of the earth taken out \[=\pi {{r}^{2}}h=\frac{22}{7}\times {{10}^{2}}\times 14\,\,{{\text{m}}^{\text{3}}}\] |
| Let the height of embankment be x metres |
| Then, Volume \[=\pi ({{R}^{2}}-{{r}^{2}})\times x,\][Where, R = 15 m, r = 10 m]\[=\frac{22}{7}({{15}^{2}}-{{10}^{2}})\times x\]\[=\frac{22}{7}\times 25\times 5\times x\] |
| Clearly, \[\frac{22}{7}\times 25\times 5\times x=\frac{22}{7}\times {{10}^{2}}\times 14\] |
| \[\Rightarrow \] \[x=\frac{100\times 14}{25\times 5}=11.2\,\,\text{m}\] |
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