If b `prop a^(3)` and a increases in the ratio of 2:3 , then find in what ratio b will be increasesed .

Explanation

b `prop a^(3) rArr b =k.a^(3) ` (where K `ne` 0= variation constant ……….(1)
Now a increases in the ratio 2:3 .
putting a `xx(3a)/(2) =(3a)/(a)` in stead of a in (1) we get ,
b=k. `((3a)/(2))^(3) rArr b =k . (27a^(3) )/(8) ……….(2)`
Now , from (1) and (2) we get ,the required ratio =`(ka^(3))/((27a^(3))/(8))=(8)/(27)=8:27.`
Hence b will be increased in the ratio 8 :27 .