Double Bubble

Geometry Level 4

Two bubbles, perfectly spherical have radii 3 and 5 and are joined together with their centers 6 units apart.

If the volume shared by both the bubbles can be expressed in the form \(\large \frac{a}{b}\pi\) for coprime positive integers \(a\) and \(b\), find the value of \(\large \frac{a+1}{b}\).

Image Credit: Wikimedia.
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