Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the
(i) radius r' of the new sphere, (ii) ratio of S and S'.
(i) Radius of 1 solid iron sphere = r
`"Volume of 1 solid iron sphere "=4/3pir^3`
`"Volume of 27 solid iron spheres "=27xx4/3pir^3`
27 solid iron spheres are melted to form 1 iron sphere. Therefore, the volume of this iron sphere will be equal to the volume of 27 solid iron spheres. Let the radius of this new sphere be r'.
`"Volume of new solid iron sphere "=4/3pi(r')^3`
r' = 3r
(ii) Surface area of 1 solid iron sphere of radius r = 4πr2
Surface area of iron sphere of radius r' = 4π (r')2
= 4 π (3r)2 = 36 πr2
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