A) \[1:\sqrt{2}\]
B) \[\sqrt{2}:1\]
C) \[1:2\]
D) \[2:1\]
Correct Answer: B
Solution :
According to the question, Base of hemisphere = Base of cone i.e., radius of hemisphere = radius of cone ?(i) and height of hemisphere=height of cone ...(ii) We know that, height of hemisphere = radius of hemisphere \[\Rightarrow \]height of cone = radius of hemisphere [from Eq. (i)] \[\Rightarrow \]height of cone = radius of cone [from Eq. (ii)] Now, Curved surface area of hemisphere \[=2\pi {{r}^{2}}\] Curved surface area of cone \[=\pi \sqrt{{{r}^{2}}+{{h}^{2}}}=\pi r\sqrt{{{r}^{2}}+{{r}^{2}}}\] \[(\because r=h)\] \[=\pi r\sqrt{2{{r}^{2}}}\times =\pi r\times \sqrt{2}\,\,r=\sqrt{2}\pi \,\,{{r}^{2}}\] \[\therefore \]Ratio of curved surface areas of hemisphere and cone \[=2\pi {{r}^{2}}:\sqrt{2}\pi {{r}^{2}}=2:\sqrt{2}\times =\sqrt{2}:1\]
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