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) = Base of cone ...(i) i.e., radius of hemisphere = radius of come ...(ii) and height of cone We know that, Height of hemisphere = radius of hemisphere or height of cone = radius of hemisphere [From Eq. (i)] or height of cone = radius of cone [From Eq. (ii)] Now, curved surface area of hemisphere \[=\pi \sqrt{{{r}^{2}}+{{h}^{2}}}\] \[=\pi r\sqrt{{{r}^{2}}+{{h}^{2}}}\] \[(\because r=h)\] \[=\pi r\sqrt{2{{r}^{2}}}\] \[=\pi r\times \sqrt{2r}\] \[=\sqrt{2}\pi {{r}^{2}}\] \[\therefore \] Ratio of curved surface areas of hemisphere and cone \[=2\pi {{r}^{2}}:\sqrt{2}\pi {{r}^{2}}\] \[=2:\sqrt{2}\] \[=\sqrt{2}:1\]
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