A hemisphere and a cone have equal bases. If their heights are also equal, then the ratio of their curved surfaces will be (a) 1 : 2 (b) 2 : 1 (c) `1\ :sqrt(2)` (d) `sqrt(2)\ :1`

Explanation

C. s. A. of a Hemisphere `=2 pi r^{2}`


C s A of a cone` =pi r s`
We have equal radius of the hemisphere base and radius of cone and their height are also equal of the hemisphere` =r`


So ,height of the cone, h=r


Ratio curved surface Area `=2 pi r^{2}: pi r s`



`=2 pi r^{2}: pi r sqrt{r^{2}+h^{2}} `


`=2 pi r^{2}: pi r sqrt{r^{2}+r^{2}} `


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