Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere.

Result

S =  9.425 m2

Solution:

a=1 D=a 3=1 3=31.7321 r=D/2=1.7321/20.866 S=4π r2=4 3.1416 0.86629.4248=9.425 m2a = 1 \ \\ D = a \cdot \ \sqrt{ 3 } = 1 \cdot \ \sqrt{ 3 } = \sqrt{ 3 } \doteq 1.7321 \ \\ r = D/2 = 1.7321/2 \doteq 0.866 \ \\ S = 4 \pi \cdot \ r^2 = 4 \cdot \ 3.1416 \cdot \ 0.866^2 \doteq 9.4248 = 9.425 \ m^2



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