



 
Hi Houston, If R is the radius of the inside of the bubble and T is the thickness of the gum that forms the skin of the bubble then the radius of the bubble is R + T. Thus the volume of the bubble is
and hence
The volume of air VA in the bubble is
and hence the volume of gum (the skin of the bubble) is
But this is a constant so its derivative is zero. Hence
Hence
Now try part (c). Harley  


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