A spherical segment

A spherical section whose axial section has an angle of j = 120° in the center of the sphere is part of a sphere with a radius r = 10 cm. Calculate the cut surface.

Correct result:

S =  586.2292 cm2


α=120 r=10 cm  sinα/2=a:r  a=r sin(α/2)=10 sin(120/2)=8.66025 cm  h=rr2a2=101028.66032=5 cm  S1=2π r h=2 3.1416 10 5314.1593 cm2  S2=π a r=3.1416 8.6603 10272.0699 cm2  S=S1+S2=314.1593+272.0699=586.2292 cm2

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