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)?

Guest Mar 11, 2021

#1**+1 **

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 in^{2 }for the curved surface

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

ElectricPavlov Mar 11, 2021