A Quick Way to Find the Volume of a Dodecahedron from Surface Area

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The surface area of one dodecahedron is 9. A similar dodecahedron has a surface area of 16. What is the ratio of the volume of the first dodecahedron to the second?

I need a quick way to solve this, like for a math competition

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You do not need such a formula. Instead, analyze the scaling; surface area grows with the square and volume with the cube.