To find out how much air the soccer ball can hold when pumped to full capacity, we need to calculate the volume of the sphere (the soccer ball) using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
First, we need to find the radius from the diameter. The diameter of the soccer ball is 22 cm, so the radius \( r \) will be:
\[ r = \frac{\text{diameter}}{2} = \frac{22 \text{ cm}}{2} = 11 \text{ cm} \]
Now, we substitute the radius into the volume formula:
\[ V = \frac{4}{3} \pi (11 \text{ cm})^3 \]
Calculating \( (11 \text{ cm})^3 \):
\[ (11 \text{ cm})^3 = 11 \times 11 \times 11 = 1331 \text{ cm}^3 \]
Now, substitute this value back into the volume formula:
\[ V = \frac{4}{3} \pi (1331 \text{ cm}^3) \]
Calculating the volume:
\[ V = \frac{4 \times 1331}{3} \pi \text{ cm}^3 \] \[ V = \frac{5324}{3} \pi \text{ cm}^3 \] \[ V \approx 1774.67 \pi \text{ cm}^3 \approx 5565.17 \text{ cm}^3 \quad (\text{using } \pi \approx 3.14159) \]
Thus, the soccer ball can hold approximately:
\[ V \approx 5565.17 \text{ cm}^3 \]
Therefore, the soccer ball at full capacity can hold approximately 5565.17 cm³ of air.