Some of the question is missing, so I hope I answer the right question. We are using the chain rule.

`S(r)=4pir^2`

`(dS(r))/(dt)=4pi(2r)(dr)/(dt) = 8pir(dr)/(dt)`

And the answer to your question is

`(dV(r))/(dt)=4/3 pi (3r^2) (dr)/(dt) = 4pir^2(dr)/(dt)`

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