Calculate the total surface area and volume of a cube with a diagonal of 2√3 cm.

Let the side of the cube be equal to X cm.

Consider a right-angled triangle ABD, in which the legs AB and AD are equal to X cm, then, according to the Pythagorean theorem, the hypotenuse BD will be equal.

BD ^ 2 = AB ^ 2 + AD ^ 2 = X ^ 2 + X ^ 2 = 2 * X ^ 2.

BD = X * √2 cm.

Consider a right-angled triangle BB1D and which leg BB1 = X, and leg BD = X * √2.

Then, by the Pythagorean theorem, B1D ^ 2 = BB1 ^ 2 + BD ^ 2.

By condition, B1D = 2 * √3, then:

(2 * √3) ^ 2 = X ^ 2 + (X * √2) ^ 2.

12 = 3 * X ^ 2.

X ^ 2 = 4.

X = 2 cm.

The side of the cube is 2 cm.

Then the total area of the cube is:

Scuba = 6 * 2 * 2 = 24 cm2.

Answer: Scuba = 24 cm2.