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How do I divide the area of a sphere into 3? 2 caps at 25% of the area each and a belt of 50%.
If a sphere (like the the earth) is divided into 3 sections, 2 caps of equal area and a belt section (at the equator), at what meridian (latitude) would the two cap areas combined equal the area of the belt.
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The Surface area of a sphere is 4* Pi* Radius^2
(that's 4 times Pi times the square of the radius of the sphere).
The surface area of the spherical cap is 2*Pi*Radius*Height.
(Height is the height from the 'pole' or the top/bottom of the sphere to the cut you are making, measured along the diameter).
Formula can be found here: http://mathforum.org/dr.math/faq/formulas/faq.sphere.html
So set the equation for 4*(surface area of the cap) = Surface area of the sphere.
So 8Pi*rh=4Pi*r^2
h=r/2
If you need an angle, that's arctan (r/2)/r = arctan .5
(that's 4 times Pi times the square of the radius of the sphere).
The surface area of the spherical cap is 2*Pi*Radius*Height.
(Height is the height from the 'pole' or the top/bottom of the sphere to the cut you are making, measured along the diameter).
Formula can be found here: http://mathforum.org/dr.math/faq/formulas/faq.sphere.html
So set the equation for 4*(surface area of the cap) = Surface area of the sphere.
So 8Pi*rh=4Pi*r^2
h=r/2
If you need an angle, that's arctan (r/2)/r = arctan .5
When the two lines are t 26.3603897 north and at 26.3603897 south.
How did you come to this conclusion?
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