Cube and sphere

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

Result

S =  235.619 cm2

Solution:

S1=150 S1=6a2 a=S1/6=150/6=5 D=3⋅ a=3⋅ 5≐5 3≐8.6603 r=D/2=8.6603/2≐4.3301 S=4π⋅ r2=4⋅ 3.1416⋅ 4.33012≐235.6194≐235.619 cm2S_{1}=150 \ \\ S_{1}=6a^2 \ \\ a=\sqrt{ S_{1}/6 }=\sqrt{ 150/6 }=5 \ \\ D=\sqrt{ 3 } \cdot \ a=\sqrt{ 3 } \cdot \ 5 \doteq 5 \ \sqrt{ 3 } \doteq 8.6603 \ \\ r=D/2=8.6603/2 \doteq 4.3301 \ \\ S=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 4.3301^2 \doteq 235.6194 \doteq 235.619 \ \text{cm}^2

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