The relationship between the diagonal of a cube and its volume can be determined using the Pythagorean theorem and the formula for the volume of a cube. Let's denote the side length of the cube as s and the length of the diagonal as d. The body diagonal is the longest diagonal in the cube, and it passes through the center of the cube. Using the Pythagorean theorem, we can establish the following relationship: s2 + s2 + s2 = d2 √3s = d To find the relationship between the diagonal and the volume, we can use the formula for the volume of a cube: V = s3 By substituting the value of s from the relationship above, we get: This equation shows that the volume of a cube is related to the diagonal by a power of 3/2.