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Hi Riya, I am glad to help you.
(i) Volume of 27 solid sphere, each of radius, r = 27 x 4/3πr3 = 36πr3
According to statement,
Volume of sphere of radius r' = Volume of 27 solid spheres
⇒ 4/3π(r'3) = 36πr3
⇒ (r')3 = 27r3 = (3r)3 ⇒ r' = 3r
(ii) We have,
S' = 4πr'2 = 4π(3r)2 = 36πr2
∴ S/S' = 4πr2 /36πr2 = 1/9
⇒ S : S' = 1 : 9
So Radius r' of the new sphere is 3r
And Ratio of S and S' is 1:9.
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