Tropics and polar zones

What percentage of the Earth’s surface lies in the tropical, temperate and polar zone?
Individual zones are bordered by tropics 23°27' and polar circles 66°33'

Correct result:

p1 =  39.7949 %
p2 =  51.9459 %
p3 =  8.2592 %


T=23+27/60=46920=23.45 P=66+33/60=133120=66.55  r=1 cos(90P)=x1:r x1=r cos((90P) rad)=r cos((90P) π180 )=1 cos((9066.55) 3.1415926180 )=0.91741 h1=rx1=10.91740.0826  cos(90T)=x2:r x2=r cos((90T) rad)=r cos((90T) π180 )=1 cos((9023.45) 3.1415926180 )=0.39795 h2=rx2=10.39790.6021  S1=2π r h1=2 3.1416 1 0.08260.5189 S2=2π r h2=2 3.1416 1 0.60213.7828  S3=2π r2=2 3.1416 126.2832  p1=100 S3S2S3=100 6.28323.78286.2832=39.7949%
p2=100 S2S1S3=100 3.78280.51896.2832=51.9459%
p3=100 S1S3=100 0.51896.2832=8.2592%

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