# 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?

Result

p =  63.662 %

#### Solution:

$r=12 \ \\ S_{1}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 12^2 \doteq 1809.5574 \ \\ a=2 \cdot \ r/\sqrt{ 3 }=2 \cdot \ 12/\sqrt{ 3 } \doteq 8 \ \sqrt{ 3 } \doteq 13.8564 \ \\ S_{2}=6 \cdot \ a^2=6 \cdot \ 13.8564^2=1152 \ \\ p=S_{2}/S_{1} \cdot \ 100=1152/1809.5574 \cdot \ 100 \doteq 63.662 \doteq 63.662 \%$

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