A) 10 m
B) 11 m
C) 11.2 m
D) 11.5 m
Correct Answer: C
Solution :
Radius of the base of well\[=\frac{20}{2}=10\,\,m\] Volume of the earth taken out \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\times {{10}^{2}}\times 14\,\,{{m}^{3}}\] 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, \[\frac{22}{7}\times 25\times 5\times x=\frac{22}{7}\times {{10}^{2}}\times 14\] \[\Rightarrow \] \[x=\frac{100\times 14}{25\times 5}=11.2\,\,m\]
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