To solve this problem, we need to understand what \( v\left(\frac{5}{7}\right) \) represents in the context of the function \( v(r) = \frac{4}{3} \pi r^3 \).
The function \( v(r) = \frac{4}{3} \pi r^3 \) calculates the volume of a sphere (or in this case, a rubber ball) given its radius \( r \).
Let's analyze the given expression \( v\left(\frac{5}{7}\right) \):
1. First, the expression \( v\left(\frac{5}{7}\right) \) means that we need to substitute \( r = \frac{5}{7} \) into the volume formula.
2. Next, when we substitute \( r = \frac{5}{7} \) into the volume formula, we compute \( v\left(\frac{5}{7}\right) = \frac{4}{3} \pi \left(\frac{5}{7}\right)^3 \).
3. The result of this computation represents the volume of the sphere (or rubber ball) when the radius is \( \frac{5}{7} \) feet.
From the provided numerical result, we know that this computed volume is approximately \( 1.526527042560638 \) cubic feet.
Thus, \( v\left(\frac{5}{7}\right) \) represents the volume of the rubber ball when the radius equals \( \frac{5}{7} \) feet.
So the correct interpretation is:
- The volume of the rubber ball when the radius equals [tex]\(\frac{5}{7}\)[/tex] feet.
