SOLUTION: Calculate the volume of a cube that has a surface area of 12cm?

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Question 148364: Calculate the volume of a cube that has a surface area of 12cm?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
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%5E2, then the total surface area of the cube is 6x%5E2 and, you are told that this is 12 cm, so...
6x%5E2+=+12 Solve for x. Divide both sides by 6.
x%5E2+=+2sq.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%282%29cm
Now that you have the length of one edge of the cube, you can find its volume by cubing this.
V+=+%28sqrt%282%29%29%5E3
V+=+2sqrt%282%29 cu.cm. This is the exact volume of the cube.
If you want the approximate value, find the square root of 2.
V+=+2%281.414%29
V+=+2.83cu.cm.