Question

9.
Twenty seven solid iron spheres, each of radius r and surface area S are melted to
for a sphere with surface area S'. Find the
radius r' of the new sphere, (i) ratio of S and S'.​

Answer 1

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Answer: S : S' = 1 : 9

Step-by-step explanation:

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