A cube is inscribed in a ball with a radius of 2√3. Find the sum of the lengths of all edges of the cube.

The diagonal of a cube is equal to the diameter of the ball circumscribed around it.
Let’s determine its size:
d cube = 2 * R ball = 2 * 2 * √3 = 4 * √3.

Find the edge of the cube using the formula:
d² = 3 * a²;
a² = d² / 3 = (4 * √3) ² / 3 = (16 * 3) / 3 = 16.
a = √16 = 4.

The cube has 12 edges. Let’s find the total length of the edges:
12 * a = 12 * 4 = 48.

Answer: the sum of the lengths of all the edges of the cube is 48.