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 answer:

p =  63.662 %

Step-by-step explanation:

$$\begin{gathered} r=12\text{ cm } \\ {S}_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 12^2\doteq 1809.5574{\text{cm}}^2 \\ a=2\cdot r\mathrm{/}\sqrt{3}=2\cdot 12\mathrm{/}\sqrt{3}=8\sqrt{3}\text{ cm}\doteq 13.8564\text{ cm } \\ {S}_2=6\cdot a^2=6\cdot 13.8564^2=1152\text{ cm } \\ p=S_2\mathrm{/}{S}_1\cdot 100=1152\mathrm{/}1809.5574\cdot 100=63.662\mathrm{\%} \end{gathered}$$

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