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math-calculus

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A spherical party balloon is being inflated with helium pumped in at a rate of 12 cubic feet per minute. How fast is the radius growing at the instant when the radius has reached 1 ft?

  • math-calculus -

    V = (4/3)πr^3
    dV/dt = 4π r^2 dr/dt
    given : dV/dt = 12 , and r = 1

    12 = 4π (1) dr/dt
    dr/dt = 3/π ft/min

  • math-calculus -

    Thank you! I initially thought the given rate of 12 cubic feet per minute was dr/dt.

  • math-calculus -

    The units are usually your give-away.

    it says 12 cubic feet/min which is volume/time , so dV/dt

    This will work in most cases.

  • math-calculus -

    12

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