Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area `\ Sprimedot` Find the (i) radius `rprime` of the new sphere, (ii) ratio of `S"\ "a n d"\ "Sprimedot`

Explanation

(i) Radius of 1 solid iron sphere` =r`
Volume` =4/3pir^3`
Volume of 27 solid iron spheres,`=27xx4/3pir^3`
`4/3pir'^3=27xx4/3pir^3`
`r'^3=2pir^3`
`=>r'=3r`
ii) Surface area`=4pir^2`
`SAr'=4pir'^2`
`=>4pi(3r)^2=36pir^2`
`S/S'=4pir^2/36pir^2=1/9=1:9`