Air is being pumped into a spherical balloon at a rate of 5 cm3/min. Determine the rate at which the radius of the balloon is increasing when the diameter of the balloon is 20 cm.(adsbygoogle = window.adsbygoogle || []).push({});

So, to solve, I know HOW to do it, I just don't know WHY it's right.

[itex]\frac{dv}{dr}=4pi r^{2}[/itex]

[itex]\frac{dv}{dt}=5cm^{3}/s[/itex]

= [itex]\frac{dv}{dt}=4pir^{2}\frac{dr}{dt}[/itex]

Solve for dr/dt

Where does dr/dt come from? I can't understand how it makes sense. It seems as if we're just pulling it out of the air.

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# Question about the application of the chain rule

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