To analyze the options provided in relation to the function \( V(r) = \frac{4}{3} \pi r^3 \):
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Volume (V) represents the amount of space inside the rubber ball, which is dependent on the radius \( r \).
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Five-sevenths in the context given could refer to a specific measurement related to either volume or radius, depending on how it is used.
Now let's evaluate the possible interpretations:
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Option 1: "the radius of the rubber ball when the volume equals five-sevenths cubic feet" implies that you're solving for \( r \) such that \( V(r) = \frac{5}{7} \).
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Option 2: "the volume of the rubber ball when the radius equals five-sevenths feet" implies that you are substituting \( r = \frac{5}{7} \) into the volume formula to find \( V\left(\frac{5}{7}\right) \).
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Option 3: "that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet" implies evaluating the volume when \( r = 7 \) (which yields \( V(7) = \frac{4}{3} \pi (7^3) \)).
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Option 4: "that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet" implies evaluating the volume when \( r = 5 \) (which yields \( V(5) = \frac{4}{3} \pi (5^3) \)).
Among these options, Option 2 is the most straightforward and correct interpretation of \( V \) and five-sevenths: it represents the volume of the rubber ball when the radius equals \( \frac{5}{7} \) feet.
Therefore, the correct choice is: the volume of the rubber ball when the radius equals five-sevenths feet.