The diagonal of the cube is 12cm. Find its volume?

The diagonal of the prism is found by the formula d = a ^ 2 + b ^ 2 + c ^ 2, where a – length, b – width, c – height
Since this is a cube, then all three quantities are equal, which means d ^ 2 will be equal to a ^ 2 * 3, i.e.
12 ^ 2 = a ^ 2 * 3
144 = a ^ 2 * 3
48 = a ^ 2
a = 4 roots of 3
the volume of the cube is a ^ 3 = (4 roots of 3) ^ 3 = 64 * 3 roots of three = 192 roots of three