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 Question from alexis, a student: a cube has one face that is equal to the total surface area of another cube. Find the ratio of their volumes

Hi Alexis,

For any cube if the side length is $x$ units then the area of each face is $x^2$ square units and its volume is $x^3$ cubic units.

Suppose the smaller of your two cubes has a side length of $s$ units. It has $6$ faces so the its surface area is $6 x^2$ square units. Thus each face of the larger of the two cubes has an area of $6 x^2$ square units. What is the side length of this cube? What is its volume?

Write back if you need further assistance,
Penny

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