Two soap bubbles are stuck together with an intermediate film separating them. Compute the radius of curvature of this film given that the radii of the bubbles in this arrangement are `r_(1)` and `r_(2)` respectively. If `r_(1) gt r_(2)` state clearly which way the intermediate film will bulge.
For the case when `r_(1)=r_(2)=2cm` calculate he radius of the bubble formed by bursting the intermediate film. The volume of a spherical dome of radius `R` and height `h` is `pib^(2)(3R-b)//3`.

Explanation

To solve the problem of the two soap bubbles stuck together with an intermediate film, we will follow these steps:

### Step 1: Understand the Configuration
We have two soap bubbles with radii \( r_1 \) and \( r_2 \). The intermediate film separates them. The pressure inside a soap bubble is given by the equation:
\[ P = \frac{4\sigma}{r} \]
where \( \sigma \) is the surface tension of the soap solution and \( r \) is the radius of the bubble.
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