Whole surface area of a solid hemisphere is equal to the curved surface area of a solid sphere. Find the ratio of lenghts of radius of hemisphere and sphere.

Explanation

Let the radius of the solid hemisphere be `r_(1)` unit and radius of the solid sphere be `r_(2)` unit.
`therefore` the whole surface area of the solid hemisphere `=3pir_(1)^(2)` sq-unit and the curved surface area of the solid sphere=`4pir_(2)^(2)` sq-unit
As per question, `3pir_(1)^(3)=4pir_(2)^(2) rArrr_(1)^(2)/(r_(2)^(2))=(4)/(3)rArr((r)/(r_(2)))^(2)=((2)/(sqrt3))=2:sqrt(3).`
Hence the required ratio=`2:sqrt(3).`