The diagonal of the cube is 6√3 cm. Determine the volume of the cube.

To calculate the volume of a cube, apply the formula V = a ^ 3.

The volume of a cube is equal to the cube of its side.

We know from the condition only the length of the cube diagonal and it is equal to 6√3 cm.

We start by finding the side of the cube.

To do this, apply the formula:

d ^ 2 = a ^ 2 + a ^ 2 + a ^ 2;

d ^ 2 = 3a ^ 2;

Substitute the value of the diagonal and solve the resulting equation:

(6√3) ^ 2 = 3a ^ 2;

108 = 3a ^ 2;

a ^ 2 = 36;

a = 6 cm (we discard the negative root of the equation, since the length of the side of the cube cannot be negative).

V = 6 ^ 3 = 216 cm ^ 3.