Sphere Packed in Box

A spherical basketball is packed in a cubical box into which it fits exactly. What percent of the volume of the box is used up by the basketball?


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v(box) = (2r)3 = 8r3

v(sphere) = 4/3 pir3

The ratio  sphere  =  4/3 pir3  =  4pi  =  pi
box 8r3

24 6

%:  pi  =  x  → x ≈ 52.4%.
6 100

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