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

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