How fast the bubble's skin grows

MediumCalculus~5m

A spherical bubble's radius grows at $\dfrac{9}{4\pi}$ inches per second. At the instant its volume is increasing at $36$ cubic inches per second, at what rate (in square inches per second) is its surface area increasing?

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$\tfrac{dV}{dt}=4\pi r^2\tfrac{dr}{dt}=9r^2$ . Set it to $36$ to find $r$ .
Then $\tfrac{dA}{dt}=8\pi r\tfrac{dr}{dt}$ with $r=2$ .

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How fast the bubble's skin grows

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