A) 4 units
B) \[\frac{1}{4}\] unit
C) 9 Units
D) \[\frac{1}{9}\]unit
Correct Answer: D
Solution :
If radius be r units and height be h units, then slant height \[I\]= \[\sqrt{{{h}^{2}}+{{r}^{2}}}\] \[\therefore \]\[\frac{1}{3}\pi {{r}^{2}}h=\pi rl\] \[\Rightarrow \] \[rh=31=3\sqrt{{{h}^{2}}+{{r}^{2}}}\] On squaring, \[{{r}^{2}}{{h}^{2}}=9({{h}^{2}}+{{r}^{2}})\] \[\Rightarrow \]\[\frac{{{h}^{2}}+{{r}^{2}}}{{{r}^{2}}\,\,\,{{h}^{2}}}=\frac{1}{9}\] \[\Rightarrow \]\[\frac{1}{{{r}^{2}}}+\frac{1}{{{h}^{2}}}=\frac{1}{9}\] units
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