If a soap bubble of radius 3 cm coalesce under isothermal conditions with another soup bubble of radius 4 cm, find the radius of the big soap bubble so formed.

Explanation

To solve the problem of finding the radius of the big soap bubble formed when two smaller soap bubbles coalesce, we can follow these steps:

### Step 1: Understand the Surface Energy Concept
When two soap bubbles coalesce, the total surface energy of the resulting bubble is equal to the sum of the surface energies of the individual bubbles. The surface energy (E) of a soap bubble is given by the formula:
\[ E = 8 \pi R^2 \]
where \( R \) is the radius of the bubble.

### Step 2: Define the Radii
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