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 $$\large \frac{a+1}{b}$$.

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