Cube and Sphere Surface Area and Relative Size
Will a sphere that has the identical surface area as a cube fit
inside the cube?
No. The surface of a sphere is 4*pi*r^2, where r is the radius, or
pi*d^2, where d is the diameter. The surface of a cube is 6*D^2,
where D is the length of any side. If pi*d^2 = 6*D^2, then
d = sqrt(6/pi) * D ~ 1.38 * D.
Advanced Photon Source, Argonne National Lab.
Click here to return to the Mathematics Archives
Update: June 2012