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9. Twenty seven solid iron spheres, each of radius r and surfaa area S are melted to form a sphere with surfaa area S Find the (i) rczdius r' of the new sphere, (ii) ratio of s and s

9. Twenty seven solid iron spheres, each of radius r and surfaa area S are melted to form a sphere with surfaa area S Find the
(i) rczdius r' of the new sphere, (ii) ratio of s and s

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
10 months ago
Tot.al volume of 27 sphere = 27 x 4 4 nr3 = 36nr3 3 (i) Volume of a new sphere = 3nr'3 •••(i) 4 .. 3nr'3 = 27 x 4 3nr3 r's = 27r3 r' = 3r (ii) Surface area of each of 27 spheres (S) = 4nr2 ...(a) Surface area of a new sphere ($') = 41t(3r)2 = 3Gn:r2 ••.(b) From (a) and (b), we get S 4nr2 1 S' = 367tr 2 = 9 Hence, S : S' = 1 : 9.

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