Given that the surface area of a cube is 384 cm^2
We need to find the length of the side of the cube.
Let us assume that the side is x cm.
Then we know that the area of one of the cube faces is x^2.
But, the cube has 6 faces.
Then the total surface area is given by 6*x^2
But we know that the surface area is 384 cm^2
==> 6x^2 = 384
Now we need to solve for x.
We will divide by 6.
==> x^2 = 384/6 = 64
Now we will take the square root of both sides.
==> x = +- sqrt64 = +-8
But we will ignore -8 because the length can not be negative value.
Then, the side of the cube is 8 cm.
A cube has equal sides, with 6 square surfaces. Therefore the area of each square surface is also equal.
So the area each surface = total surface area of the cube/6 = 384 cm^2/6 = 64 cm^2.
Therefore the length side of the the cube = sqrt(64 cm^2) = 8cm.