Question 148364
The total surface area of a cube consists of the sum of the areas of each of the six faces.
If the area of one face is {{{x^2}}}, then the total surface area of the cube is {{{6x^2}}} and, you are told that this is 12 cm, so...
{{{6x^2 = 12}}} Solve for x. Divide both sides by 6.
{{{x^2 = 2}}}sq.cm. This is the area of one face, and, since the faces are squares, you can find the length of one side of the face by taking the square root.
{{{x = sqrt(2)}}}cm
Now that you have the length of one edge of the cube, you can find its volume by cubing this.
{{{V = (sqrt(2))^3}}}
{{{V = 2sqrt(2)}}} cu.cm.  This is the exact volume of the cube.
If you want the approximate value, find the square root of 2.
{{{V = 2(1.414)}}}
{{{V = 2.83}}}cu.cm.