Spherical section cut

Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees.

Correct result:

V =  1007.6663 cm3

Solution:

ρ=10 cm ω=120  sinω/2=ρ/r s=sin(ω/2)=sin(120/2)=0.86603  r=ρ/s=10/0.86611.547 cm  h=rr2ρ2=11.54711.54721025.7735 cm  V=π6 h (3 ρ2+h2)=3.14166 5.7735 (3 102+5.77352)=1007.6663 cm3



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