Sphere area

A cube with an edge 1 m long is a circumscribed sphere (vertices of the cube lie on a sphere's surface). Find the surface area of the sphere.

Final Answer:

S =  9.4248 m²

Step-by-step explanation:

$$\begin{gathered} a=1\text{m} \\ {D}^2=a^2+a^2+a^2=3a^2 \\ D=a\cdot \sqrt{3}=1\cdot \sqrt{3}=\sqrt{3}\text{m}\doteq 1.7321\text{m} \\ r=D/2=1.7321/2\doteq 0.866\text{m} \\ S=4\pi \cdot r^2=4\cdot 3.1416\cdot 0.866^2=9.4248{\text{m}}^2 \end{gathered}$$

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