How do you figure out the surface area to volume ratio of a cube that has sides that are 3cm long?

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The simplest method is to compute the surface area of the cube, its volume and then find their ratio. Denote the length of a side as `b` centimeters.

The volume of a cube with the side length `b` is `b^3` (this is the base for defining volumes of more complex figures).

The surface of a cube consists of `6` congruent squares: we may call them upper, lower, left, right, front and rear. The surface of each of these squares is `b^2,` thus the surface area of a cube is `6b^2.`

So the ratio in question is equal to  `(6b^2)/(b^3) = 6/b.`

If `b = 3 cm,` the value of this ratio is  `6/(3 cm) = 2 (cm)^(-1),` which is the answer (yes, the dimension of this quantity is `(cm)^(-1) = 1/(cm)` ).

 

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