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To tackle this you first need to know the equations for both volume and surface area. The surface area of a cube is 6x2 where x is the side length. The volume of the cube is x3. Thus x is the cube root of the volume. We can substitute this in to the surface area equation and say that the surface area of a cube is 6volume2/3

This can also be rearranged to say that the volume of the cube is (the surface area/6)1.5

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Q: How do you find the direct proportion between volume and surface area of a cube?
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How does a surface area of a solid vary with its volume?

Provided the shape remains similar, the surface varies as the 2/3 power of the volume. Or, to put it another way, the cube root of the volume varies directly as the square root of the surface area. Or, the square of the volume is in direct proportion to the cube of the area.


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Direct Proportion means that as one increases, the other also increases.Inverse proportion is the reciprocal of direct proportion. If something is in the direct proportion of 1:3, then the inversion proportion is 3:1.OrIndirect Proportion means that as one increases the other decreases, or one is directly proportional to 1 divided by the other. Example: Pressure is indirectly proportional to volume, or Pressure is directly proportional to 1/Volume.


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