Spherical cap

Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.

Correct result:

r =  3.0683 cm

Solution:

D=4.6 cm R=D/2=4.6/2=2310=2.3 cm S=20 cm2  S=2 πr v cm  r2=R2+(rv)2  v22rv+R2=0 v=S2π r  r=S4π S4π2 R2=204 3.1416 204 3.14162 2.323.0683=3.0683 cm   Verifying Solution:  v=rr2R2=3.06833.068322.321.0374 cm S1=2π r v=2 3.1416 3.0683 1.0374=20 cm2 S1=S



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