Difficult to evaluate area of a spherical rectangle than that of a plane rectangle

Mar 2015
11
0
Vill-Buraura, Distt-Mahoba (UP) India-210429
How to evaluate the area covered by a spherical rectangle, having length & width (each as a great circle arc) of 18 & 6 units respectively, on a spherical surface with a radius 50 units? any help is highly appreciated. thanks in advance.......(Flower)(Flower)
 

chiro

MHF Helper
Sep 2012
6,608
1,263
Australia
Re: Difficult to evaluate area of a spherical rectangle than that of a plane rectangl

Hey hcrajpoot.

There are a few ways you could do this. You could use vector calculus results or you could deform the solid using a co-ordinate transformation and get the boundary in Euclidean space.

Here is an idea of the first method:

Pauls Online Notes : Calculus III - Surface Integrals