How fast is the balloon growing?

MediumCalculus~4m

Air is pumped into a spherical balloon at a constant $100$ cm³/s. At the instant the radius is $5$ cm, how fast is the radius increasing (in cm/s)? Give a decimal to four places.

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Differentiate $V=\tfrac43\pi r^3$ with respect to time: $\tfrac{dV}{dt}=4\pi r^2\tfrac{dr}{dt}$ .
Solve for $\tfrac{dr}{dt}$ with $\tfrac{dV}{dt}=100$ , $r=5$ .

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0.3183 (± 0.001)

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How fast is the balloon growing?

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