The surface area of a cube is 200. Find its diagonal.

We take the side of the cube as a, then the area of one face of the cube is s = a ^ 2. And the surface area of the cube, equal to the area of the six faces of the cube, is equal to:

Sk = 6 * s = 6 * a ^ 2 = 200, whence a ^ 2 = 200/6 = 100/3.

Next, we compose an expression for the diagonal of a square, which is a face of a cube, using the Pythagorean theorem:

d ^ 2 = a ^ 2 + a ^ 2 = 2 * a ^ 2 = 2 * (100/3).

Now we find the diagonal of the cube as the hypotenuse of a right-angled triangle, which consists of the side of the cube a, and the diagonal of the square d.

D ^ 2 = d ^ 2 + a ^ 2 = (2 * 100/3) + 100/3 = 100 * (3/3) = 100.

D = √100 = 10.