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As Khalid inflates a spherical balloon, Kareem wonders about its different rates. He knows that the rate at which Khalid blows is equal to the rate at which the volume changes . As the balloon inflates, other aspects are changing as well, such as the radius and the surface area.

  1. If  , calculate the rate of change of the radius, , when cm.

    Using just geometry (no Calculus), find the equation for a generic spherical balloon.

    Substitute the given information and solve.

  2. If , calculate the rate of change of the surface area, , when cm.

    Using just geometry, write the equation for the Surface Area of a generic spherical balloon:

  3. Describe is happening to the balloon when is negative.

    What does a negative rate represent?