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help on calculus

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A spherical balloon is being filled with air in such a way that its radius is increasing at a rate of 2 centimeters per second. At what rate is the volume of the balloon changing at the instant when its surface has an area of 4 pi or 12.56637061 square centimeters?

  • help on calculus -

    Volume = V = (4/3) pi r^3
    dV/dt = 4 pi r^2 dr/dt
    When the area 4 pi r^2 = 4 pi, the value of r is 1.

    At that instant,
    dV/dt = 4 pi *(1 cm^2)*2 cm/s
    = 8 pi cm^3/s

  • help on calculus -


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