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=r−r⋅ cos⁡(A∘→ rad)=r−r⋅ cos⁡(A∘⋅ π180 )=6371−6371⋅ cos⁡(23.45∘⋅ 3.1415926180 )=526.19555 h2=r−r⋅ cos⁡(B∘→ rad)=r−r⋅ cos⁡(B∘⋅ π180 )=6371−6371⋅ cos⁡(66.55∘⋅ 3.1415926180 )=3835.66927  S=4π⋅ r2/2=4⋅ 3.1416⋅ 63712/2≐255032235.955 km2  S1=2π⋅ r⋅ h1=2⋅ 3.1416⋅ 6371⋅ 526.1955≐21063699.1055 km2 S2=2π⋅ r⋅ h2=2⋅ 3.1416⋅ 6371⋅ 3835.6693≐153542506.717 km2  p1=100⋅ S1S=100⋅ 21063699.1055255032235.955=8.2592%
S3=S2−S1=153542506.717−21063699.1055=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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