A rectangular solid, or cuboid, with sides of lengths 2, 10, and 22 is inscribed in a sphere. What is the side length of the cube that can be inscribed in that sphere?
+1486 A rectangular solid, or cuboid, with sides of lengths 2, 10, and 22 is inscribed in a sphere. What is the side length of the cube that can be inscribed in that sphere?
Face diagonal (Df) of the cuboid's side 10 x 22 is:> Df = sqrt(22² + 100²) = 24.16609195
Interior diagonal (Ds) of the cuboid is:> Ds = sqrt(Df² + 2²) = 24.24871131
Ds is the diameter of a sphere and also an interior diagonal of a cube.
The side length of the cube (a) is:> a = Ds / sqrt(3) = 14 
