To calculate the amount of air the soccer ball can hold at full capacity, we need to determine 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,
- \(r\) is the radius.
Given that the diameter of the soccer ball is 8 inches, we can find the radius:
\[ r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ inches} \]
Now we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (4)^3 \]
Calculating \(4^3\):
\[ 4^3 = 64 \]
Now substituting back into the volume equation:
\[ V = \frac{4}{3} \times 3.14 \times 64 \]
First, calculate \(\frac{4}{3} \times 64\):
\[ \frac{4 \times 64}{3} = \frac{256}{3} \approx 85.33 \]
Now multiply by \(\pi\):
\[ V \approx 85.33 \times 3.14 \approx 267.69 \]
Rounding to the nearest whole number gives:
\[ 268 \]
Therefore, the soccer ball can hold approximately 268 inches³ of air.
The correct response is:
268 inches³