Cube into sphere

The cube has brushed a sphere as large as possible. Determine how much percent was the waste.

Correct result:

p =  47.6401 %

Solution:

a=1 r=a/2=1/2=12=0.5  V1=a3=13=1 V2=43⋅ π⋅ r3=43⋅ 3.1416⋅ 0.53≐0.5236  p=100⋅ V1−V2V1=100⋅ 1−0.52361=47.6401%

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