Tropics and polar zones

What percentage of the Earth's surface lies in the tropical, temperate, and polar zone?
Tropics border individual zones at 23°27' and polar circles at 66°33'.

Correct answer:

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

Step-by-step explanation:

T=23+27/60=20469=23.45  P=66+33/60=201331=66.55   r=1 cos(90P)=x1:r x1=r cos((90P)° rad)=r cos((90P)° 180π )=1 cos((9066.55)° 1803.1415926 )=0.91741 h1=rx1=1x1=10.91740.0826  cos(90T)=x2:r x2=r cos((90T)° rad)=r cos((90T)° 180π )=1 cos((9023.45)° 1803.1415926 )=0.39795 h2=rx2=1x2=10.39790.6021  S1=2π r h1=2π 1 h1=2 3.1416 1 0.08260.5189 S2=2π r h2=2π 1 h2=2 3.1416 1 0.60213.7828  S3=2π r2=2π 12=2 3.1416 126.2832  p1=100 S3S3S2=100 6.28326.28323.7828=39.7949%
p2=100 S3S2S1=100 6.28323.78280.5189=51.9459%
p3=100 S3S1=100 6.28320.5189=8.2592%

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