It is not clear what your question is here. What do you mean by "ins tuned"? Assuming you meant inscribed, I'd say looking at a cross section of the cylinder and the cube we would see a square inside of a circle. Now we need to find the length of a side of this square. We look at half of the square and see that it would be a 45-45-90 triangle with the long side having the length of the diameter of the circle, 10. A 45-45-90 triangle has a special relationship between its sides, namely, that hypotenuse = leg * √2. So the length of the leg is 10 / √2 = 7.071. Therefore the volume of the cube is 7.0713 = 353.553.