| A solid is hemispherical at the bottom and conical above. If the surface areas of two parts are equal, then the ratio of radius and height of its conical part is |
A) \[1:3\]
B) \[1:1\]
C) \[\sqrt{3}:1\]
D) \[1:\sqrt{3}\]
Correct Answer: C
Solution :
| Surface area of cone |
| = Surface area of hemisphere |
 |
| \[\pi rl=2\pi {{l}^{2}}\]\[\Rightarrow \]\[l=2r\] |
| Height of cone \[=\sqrt{{{l}^{2}}-{{r}^{2}}}\] |
| \[=\sqrt{4{{r}^{2}}-{{r}^{2}}}=\sqrt{3}r\] |
| Height of hemisphere \[=r\] |
| \[\therefore \] Ratio \[=\frac{\sqrt{3}r}{r}=\frac{\sqrt{3}}{1}=\sqrt{3}:1\] |
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