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    IBMediumCalculus10–12

    How Fast the Balloon's Radius Grows

    Com que Rapidez Cresce o Raio do Balão

    A spherical balloon is inflated at a constant rate of 50 cm350 \text{ cm}^{3} per second. Find the rate at which the radius is increasing at the moment when the radius is 1010 cm.

    Two quantities change with time and a formula ties them together. Differentiate that formula with respect to time — the chain rule is what lets a radius derivative appear inside a volume derivative.

    Solution

    Step 1 of 8

    1. 1.Volume of a sphere: