Q. 94.4( 230 Votes )
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′
Answer :
(i) Volume of new sphere having radius r’ = 
πr’3
Volume of 27 spheres having radius r = 27 × 
πr3
According to the question,
πr’3 = 27 × 
πr3
= r’3 = 27r3
= r’3 = (3r)3
r’ = 3r
(ii) Ratio of surface area = 
= 
= 
= 1: 9
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