SOLUTION: SOLID MENSURATION: the area of a lune is 4π sq m and the radius of the sphere is 3 m.find the angle of the lune.

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Question 1042847: SOLID MENSURATION: the area of a lune is 4π sq m and the radius of the sphere is 3 m.find the angle of the lune.
Answer by ikleyn(52873)   (Show Source): You can put this solution on YOUR website!
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SOLID MENSURATION: the area of a lune is 4*pi sq m and the radius of the sphere is 3 m. find the angle of the lune.
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SOLID MENSURATION: Mensuration is the mathematical name for calculating the areas, volumes, length of sides, and other geometric parts of standard 
geometric shapes such as circles, spheres, polygons, prisms, cylinders, cones, etc., through the use of mathematical equations or formulas. 
(From this WEB-page).

Spherical lune: In spherical geometry, a spherical lune is an area on a sphere bounded by two half great circles which meet at antipodal points
(see Wikipedia article. Also see Wolfram article).

The surface area of the lune is

 S = , 

where  is a dihedral angle.

Substitute here the given data, and you will get

 = ,  or

 =  radians.

Answer.   =  radians.


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