To determine how much air the exercise ball can hold when pumped to maximum capacity, we need to calculate the volume of a sphere using the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius of the sphere.
- Find the radius: The diameter of the ball is given as 20 inches. The radius \( r \) is half of the diameter:
\[ r = \frac{20}{2} = 10 \text{ inches} \]
- Calculate the volume: Plugging the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (10)^3 \]
Calculating \( 10^3 \):
\[ 10^3 = 1000 \]
Now substituting that back in:
\[ V = \frac{4}{3} \times 3.14 \times 1000 \]
Calculating \( \frac{4}{3} \times 1000 \):
\[ \frac{4 \times 1000}{3} = \frac{4000}{3} \approx 1333.33 \]
Now, multiply this by \( \pi \) (3.14):
\[ V \approx 1333.33 \times 3.14 \approx 4186.66 \]
- Rounding the volume: We round 4186.66 to the nearest tenth:
\[ V \approx 4186.7 \]
Therefore, the amount of air the exercise ball can hold when pumped to maximum capacity is approximately \( \boxed{4186.7} \) cubic inches.