To calculate the volume of the exercise ball when it is fully inflated, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
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 plug 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 that back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 1000 \]
Calculating \( \frac{4}{3} \times 3.14 \):
\[ \frac{4 \times 3.14}{3} = \frac{12.56}{3} \approx 4.1866667 \]
Now we can multiply that by 1000:
\[ V \approx 4.1866667 \times 1000 \approx 4186.6667 \]
Finally, rounding to the nearest tenth:
\[ V \approx 4186.7 \text{ inches}^3 \]
So, the exercise ball can hold approximately 4186.7 inches³ of air when pumped to maximum capacity.