Question

If the ratio of curved surface areas of two hemisphere is 4:9, then the ratio of their lenghts of radii is 2:3

Answer 1

Let the radii of the rwo spheres be `r_(1) "and" r_(2)` units.As per question,
`2pir_(1)^(2):2pir_(2)^(2)=4:9 rArr (2pir_(1)^(2))/(2pir_(1)^(2))=(4)/(9)rArr(r_(1)/(r_(2)))^(2)=((2)/(3))^(2)rArrr_(1)/r_(2)=(2)/(3)rArrr_(1):r_(2)=2:3`
Hence the given atatement is true.