Ratio of $x$ to that of $y$

Question

When someone asks for the ratio of $x$ to that of $y$, is that $\dfrac{y}{x}$ or $\dfrac{x}{y}$? It seems like it should be the second one but my book claims it is the first one.

Answer 1

I would write down the ratio as $x : y$, which is $x / y$ for many subsequent calculations, but not all (see comments).

Answer 2

In your comment you say (emphasis mine):

My question is coming from this question: A cube is inscribed in a sphere of radius r. Find the ratio of the volume of the cube to that of the sphere.

This is somewhat different from what you ask in your question. Indeed, here that refers to the volume, not to the ratio. If $V_C$ is the volume of the cube and $V_S$ is the volume of the sphere, the question is asking you to compute the ratio of $V_C$ to $V_S$. To me — and to Wikipedia, too — this means that you need to compute $$ \frac{V_C}{V_S}. $$