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A cube is inscribed within a hemisphere. (Note: being inscribed means that all 8 corners of the cube touch the surface of the hemisphere.) The cube has 2-inch edges.  What is the surface area of the hemisphere (including the bottom surface)?

 Mar 11, 2021
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Find the radius of the hemisphere....draw a line form one of the top corners to the middle of the cube face touching the flat face of the hemisphere "

    r = sqrt ( 2^2 + 1^2 + 1^2)   =  sqrt 6

 

surface area of 1/2 of a sphere   =   1/2   4 pi ^2    =    2 pi (sqrt6)2  =   12 pi  in2     for the curved surface

                                                                                                    PLUS pi r^2  = pi (sqrt6)^2 = 6pi  in2   for the flat surface of the hemisphere

 Mar 11, 2021

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