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How to Inscribe a Sphere in a Cube

Inscribing is the process of enclosing a two- or three-dimensional body within another body. To fulfill the requirements for inscribing, the shell of the inner body must touch the outer body. One or more dimensions are then shared by both bodies. A sphere enclosed by a cube shares the center point of the cube. The sphere touches the outer cube in six places, at the center of every cube face. The distance between opposite faces of a cube is the cube's side length. This distance is also the diameter of the sphere.

Ruler

Instructions

- 1
  Draw a cube using the ruler. A cube has six square sides, all of which have identical dimensions. Let the side length, measured from corner to corner along an edge of the cube, be represented by L.
- 2
  Use the ruler to draw four diagonal lines joining opposite corners of the cube. The four lines intersect in the middle of the cube. Label the point of intersection as M. The center of the cube will also serve as the center of the inscribed sphere.
- 3
  Draw a sphere with radius (L/2) that is centered on M. The radius is the distance from the center of the sphere to its outer edge. The sphere will touch the cube in the middle of each of the six faces of the cube. However, the sphere will not reach the corners of the cube.

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