Editing Spherical cap (section)

=== Surface area bounded by parallel disks ===

The curved surface area of the [[spherical segment]] bounded by two parallel disks is the difference of surface areas of their respective spherical caps. For a sphere of radius <math>r</math>, and caps with heights <math>h_1</math> and <math>h_2</math>, the area is

:<math>A=2 \pi r |h_1 - h_2|\,,</math>

or, using geographic coordinates with latitudes <math>\phi_1</math> and <math>\phi_2</math>,<ref>{{cite book|title=Successful Software Development|author=Scott E. Donaldson, Stanley G. Siegel|url=https://books.google.com/books?id=lrix5MNRiu4C&pg=PA354|access-date=29 August 2016|isbn=9780130868268|year=2001}}</ref>

:<math>A=2 \pi r^2 |\sin \phi_1 - \sin \phi_2|\,,</math>

For example, assuming the Earth is a sphere of radius 6371&nbsp;km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016<ref>{{cite web|url=http://www.neoprogrammics.com/obliquity_of_the_ecliptic/ |title=Obliquity of the Ecliptic (Eps Mean) |publisher=Neoprogrammics.com |access-date=2014-05-13}}</ref>) is {{math|1= 2''π''{{thinsp}}&sdot;{{thinsp}}6371<sup>2</sup>{{thinsp}}{{abs|sin 90° &minus; sin 66.56°}}}} = {{convert|21.04|e6km2|e6mi2|abbr=unit}}, or {{math|1= 0.5{{thinsp}}&sdot;{{thinsp}}{{abs|sin 90° &minus; sin 66.56°}}}} = 4.125% of the total surface area of the Earth.

This formula can also be used to demonstrate that half the surface area of the Earth lies between latitudes 30° South and 30° North in a spherical zone which encompasses all of the [[tropics]].