question_answer

A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surface will be

A) \[1:\sqrt{2}\]                 

B) \[\sqrt{2}:1\]

C) 1 : 2                             

D) 2 : 1

Correct Answer: B

Solution :

Slant height of the cone   \[=\sqrt{{{r}^{2}}+{{r}^{2}}}\] \[=\sqrt{2}r\] \[\therefore \] Ratio of their curves surface are             \[2\pi {{r}^{2}}:\pi r\times \sqrt{2r}\]             \[2\pi {{r}^{2}}:\sqrt{2}\pi {{r}^{2}}=\sqrt{2}:1\]