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 we cut the spherical cap.

Correct answer:

r =  3.0683 cm

Step-by-step explanation:

D=4.6 cm R=D/2=4.6/2=1023=2.3 cm S=20 cm2  S =  2 π r   v  cm  r2 = R2 + (rv)2  v2  2rv + R2 = 0 v =  2π rS  r=4π S4π2 R2S=4 3.1416 204 3.14162 2.32203.0683 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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