Tropical, mild and arctic

How many percents of the Earth's surface lies in the tropical, mild and arctic range? The border between the ranges is the parallel 23°27 'and 66°33'.

Correct result:

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

Solution:

A=23+27/60=46920=23.45  B=66+33/60=133120=66.55  r=6371 km  h1=rr cos(A rad)=rr cos(A π180 )=63716371 cos(23.45 3.1415926180 )=526.19555 h2=rr cos(B rad)=rr cos(B π180 )=63716371 cos(66.55 3.1415926180 )=3835.66927  S=4π r2/2=4 3.1416 63712/2255032235.955 km2  S1=2π r h1=2 3.1416 6371 526.195521063699.1055 km2 S2=2π r h2=2 3.1416 6371 3835.6693153542506.717 km2  p1=100 S1S=100 21063699.1055255032235.955=8.2592%
S3=S2S1=153542506.71721063699.1055=132478807.611 km2 p2=100 S3S=100 132478807.611255032235.955=51.9459%
p3=100(p1+p2)=100(8.2592+51.9459)=39.7949%



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