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Question

A big RED spherical balloon (radius = 6a) is filled up with gas. On this balloon six small GREEN spherical balloons (radius = a) are stuck on the surface in a specific manner. As RED balloon is slowly deflated, a point comes when all these six GREEN balloons touch and green balloons arrange themselves in a 3-D closed packing arrangement. At that stage the radius of the RED balloon would have reduced by approximately:

A
14.5 times
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B
9.7 times
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C
6.0 times
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D
2.4 times
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Solution

The correct option is A 14.5 timesr+r−=0.414 for octahedral void fitted with our red spherical balloon r+a=0.414 r+=0.414a Initial r+ radius=6a Final r+ radius=0.414a Initial rFinal r=6a0.414a=14.49 or 14.5

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