To find the volume of the exercise ball, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
- Calculate the radius: The diameter of the ball is 20 inches, so the radius \( r \) is half of that:
\[ r = \frac{20}{2} = 10 \text{ inches} \]
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Substitute the radius into the volume formula: \[ V = \frac{4}{3} \times 3.14 \times (10)^3 \]
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Calculate \( (10)^3 \): \[ (10)^3 = 1000 \]
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Now calculate the volume: \[ V = \frac{4}{3} \times 3.14 \times 1000 \]
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Calculate \( \frac{4}{3} \times 3.14 \): \[ \frac{4}{3} \times 3.14 \approx 4.18667 \]
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Now, multiply by 1000: \[ V \approx 4.18667 \times 1000 \approx 4186.67 \]
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Round to the nearest tenth: \[ V \approx 4186.7 \text{ inches}^3 \]
Therefore, the exercise ball can hold approximately 4186.7 inches³ of air when pumped to maximum capacity.