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Balloon related rates

MediumCalculus~5m

A spherical balloon's volume grows at 4 cm3/s4\text{ cm}^3/\text{s}. How fast is the radius growing (in cm/s) when r=2r=2 cm? (to 3 decimals)

Show hints (2)+
  1. Differentiate V=43πr3V=\tfrac43\pi r^3 in time.
  2. Solve dV/dt=4πr2 dr/dtdV/dt = 4\pi r^2\,dr/dt for dr/dtdr/dt.

Answer

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0.0796 (± 0.002)

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