Question

The ratio of the volumes of two spherers is 216 : 125. If the sum of the radii of the two sphere be 22 cm , then find the radii pf the spheres.

Answer 1

Let the radii of the two spheres be `r_(1)`cm and `r_(2)` cm respectively.
As per question ,`(4)/(3)pir_(1)^(3):(4)/(3)pir_(1)^(3)=216:125rArr(r_(1)/(r_(2))^(3))=(216)/(125)=((6)/(5))^(3)`
`rArr r_(1)/r_(2)=(6)/(5)rArr r_(1)=(6r_(2))/(5)………..`(1)
Again, by question, `r_(1)+r_(2)=22`
`rArr (6r_(2))/(5)+r_(2)=22 [by (1)]rArr 11 r_(2)=22xx5 rArr r_(2)=(22xx5)/(11)=10`
`:.` from (1) we get, `r_(1)=(6xx10)/(5)`=12.
Hence the radii of the two sphere were 10 cm and 12 cm respectively.