# When a soap bubble is blown inside another soap bubble why does the outer bubble not increase in size?

We blow one soap bubble with volume of air trapped ( say x) . We blow another bubble inside this bubble by blowing additional volume of air ( say y). So now the volume of air inside the first bubble is X + Y which is higher than x. But this additional volume does not make the size of the outer bubble change, it remains the same even when the second bubble inside is blown. why does this happen?

If we imagine a sphere with radius $R$ (the original bubble), and we want to put a new bubble inside with radius $R/2$, how big will the original bubble be? All we need to know is that it's proportional to the cube of the radius.
$$V = k R^3$$ $$V' = k R^3 + k (R/2)^3$$ $$V' = 1.125 k R^3$$ $$V' = k (1.04 R)^3$$