2
$\begingroup$

How do I calculate the surface area of the unit sphere above the plane $z=\frac12$?

EDIT: I have been attempting things and I am thinking about parameterizing this... While I know that surface area is given by the double integral of the cross products of partial derivatives of the new parameters, I don't know what to set them to.. (sorry I'm not good with the fancy notation)

  • 0
    If you just want a formula, [Wikipedia has it](https://en.wikipedia.org/wiki/Spherical_cap). MathWorld has [a derivation as well](http://mathworld.wolfram.com/Zone.html).2012-06-03

4 Answers 4