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Let's say I have a football of radius r1 inflated to pressure p1 and insert a solid metal ball of radius r2 (without losing any air), to give a new pressure of p2.

Is there a formula I can use that gives me p2 in terms of r1, r2 and p1?

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closed as off-topic by Aaron Stevens, ZeroTheHero, Buzz, Kyle Kanos, Jon Custer Jan 7 at 14:35

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If this is carried out without any change in temperature(isothermally)(which is a very good approximation), you can use

$P_1V_1=P_2V_2$

Use $V_1$ as initial volume of balloon(spherical) and $V_2$ as the final volume of air remaining.

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