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Question

27 metal balls each of radius r are melted together to form one big sphere of radius R. Then the ratio of surface area of the big sphere to that of a ball is __________.

A
9:1
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B
3:2
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C
27:5
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D
3:1
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Solution

The correct option is A 9:1
Volume of 27 metal balls of radius r, V1=27×43πr3=36r3π
Volume of sphere of radius R, V2=43R3π
V1=V2
36r3π=43R3πR3r3=27
R=3r
Thus, S1S2=4πR24πr2=91

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