To calculate the volume of a soccer ball at full capacity, we treat it as a sphere and use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
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Find the radius: The diameter of the soccer ball is 8 inches, which means the radius \( r \) is half of the diameter: \[ r = \frac{8}{2} = 4 \text{ inches} \]
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Substitute into the volume formula: Now plug the radius into the volume formula. \[ V = \frac{4}{3} \cdot 3.14 \cdot (4)^3 \]
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Calculate \( (4)^3 \): \[ (4)^3 = 64 \]
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Calculate the volume: \[ V = \frac{4}{3} \cdot 3.14 \cdot 64 \]
First, calculate \( \frac{4}{3} \cdot 64 \): \[ \frac{4}{3} \cdot 64 = \frac{256}{3} \approx 85.33 \]
Now multiply by \( 3.14 \): \[ V \approx 85.33 \cdot 3.14 \approx 267.76 \]
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Round to the nearest whole number: \[ V \approx 268 \text{ inches}^3 \]
Therefore, the soccer ball can hold approximately 268 inches cubed of air when pumped to full capacity. So the correct response is:
268 inches³