Cube and sphere

Cube with the surface area 150 cm² is described sphere. What is sphere surface?

Correct answer:

S =  235.6194 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=150 \\ {S}_1=6a^2 \\ a=\sqrt{S_1\mathrm{/}6}=\sqrt{150\mathrm{/}6}=5 \\ D=\sqrt{3}\cdot a=\sqrt{3}\cdot 5=5\sqrt{3}\doteq 8.6603 \\ r=D\mathrm{/}2=8.6603\mathrm{/}2\doteq 4.3301 \\ S=4\pi \cdot r^2=4\cdot 3.1416\cdot 4.3301^2=235.6194{\text{cm}}^2 \end{gathered}$$

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