The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio between the volume of the first and the second bubble?

Explanation

To solve the problem, we need to find the ratio of the volumes of two soap bubbles based on the given excess pressures. Let's break it down step by step.

### Step 1: Understand the relationship between excess pressure and radius
The excess pressure \( P \) inside a soap bubble is given by the formula:
\[ P = \frac{4S}{r} \]
where \( S \) is the surface tension of the soap solution and \( r \) is the radius of the bubble.
...