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)?
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