You have to solve the following equation:
x3 = 360cm3
x = 3sqrt(360cm3) = 7.11cm.
That is, a cube 7.11 cm in length. Note that you have to take the 3rd root of 360 to get the answer.
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The volume of a cube is determined by cubing the length of one edge, so the cube root of the volume will give you the length of an edge. (In a cube, all of the edges are the same length)
Multiply its length three times as for example length*length*length will give you the answer in cubic inches
Any one dimension increased by 2, or any two dimensions increased by the square root of 2 orall three dimensions increased by the cube root of 2.
Any one dimension increased by 3, or any two dimensions increased by the square root of 3 or all three dimensions increased by the cube root of 3.
The answer depends on what information you have about the cube. If, for example, you know the volume, V, then the surface area is 6*cuberoot(V)^2. If you have the lengths of an edge, s, then it is 6*s^2.