Question #c45e4

1 Answer
P dilip_k
Sep 17, 2016

The surface area bounded by two circles of latitude is the difference of surface areas of their respective spherical caps. For a sphere of radius r, and latitudes #phi_1 and phi_2# the area is

#A=2pir^2abs(sinphi_2-sinphi_1)#

Inserting

#phi_1=-45^@ " for south and " phi_2=+45^@" for north "# we get

#A=2pir^2abs(sin(45^@)-sin(-45^@))=2sqrt2pir^2#

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