The diameter of the ball described about the cube is equal to the root of 6 cm. Find the sum of the edges of the cube.

Since a ball (or sphere) is described around the cube, the diameter of the ball is equal to the diagonal of the cube d.

d = a * √3, where a is the edge of the cube.

Let’s find the length of the edge of the cube:

a = d / √3 = √6 / √3 = √ (6/3) = √2 (cm).

Since there are 12 edges in the cube, which are equal, then their sum will be equal to:

12 * a = 12 * √2 = 12√2 (cm).

Answer: the sum of the edges of the cube is 12√2 cm.