Sphere vs cube

How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?

Correct result:

p =  63.662 %

Solution:

r=12 S1=4π⋅ r2=4⋅ 3.1416⋅ 122≐1809.5574 a=2⋅ r/3=2⋅ 12/3=8 3≐13.8564 S2=6⋅ a2=6⋅ 13.85642=1152 p=S2/S1⋅ 100=1152/1809.5574⋅ 100=63.662%

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