To calculate the volume of the exercise ball when it is at maximum capacity, we can use the formula for the volume \( V \) of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
Given that the diameter of the ball is 20 inches, we can find the radius by dividing the diameter by 2:
\[ r = \frac{20}{2} = 10 \text{ inches} \]
Now, we can substitute the radius into the volume formula. Using \( \pi \approx 3.14 \):
\[ V = \frac{4}{3} \times 3.14 \times (10)^3 \]
Calculating \( (10)^3 \):
\[ (10)^3 = 1000 \]
Now substituting:
\[ V = \frac{4}{3} \times 3.14 \times 1000 \]
First, calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4 \times 3.14}{3} \approx \frac{12.56}{3} \approx 4.1867 \]
Now multiply by 1000:
\[ V \approx 4.1867 \times 1000 \approx 4186.7 \]
Now, rounding to the nearest tenth, we find:
\[ V \approx 4186.7 \]
Thus, the volume of air the exercise ball can hold when pumped to maximum capacity is approximately:
\[ \boxed{4186.7} \text{ inches}^3 \]