The ratio of the volumes of two cubes is 729 : 1331.

If volume ratio is $x^3: y^3$, the side ratio is $x: y$ and surface area ratio is $x^2: y^2$. Given $729 = 9^3$ and $1331 = 11^3$, side ratio is $9: 11$ and area ratio is $9^2: 11^2 = 81: 121$.

Students often forget to take the cube root of the volume ratio first and instead square the volume ratio directly or confuse volume/area units.

This concept of scaling ratios applies to all similar 3D figures: if the linear ratio is $k$, the area ratio is $k^2$ and the volume ratio is $k^3$.