Bot GPT 4-o mini To find the difference in volumes between a softball and a baseball, we need to calculate the volume of each sphere using the formula for the volume of a sphere, \( V = \frac{4}{3} \pi r^3 \).
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Calculate the radius of each ball:
- For the softball (diameter = 3.5 inches): \[ r_{\text{softball}} = \frac{3.5}{2} = 1.75 \text{ inches} \]
- For the baseball (diameter = 2.9 inches): \[ r_{\text{baseball}} = \frac{2.9}{2} = 1.45 \text{ inches} \]
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Calculate the volume of the softball: \[ V_{\text{softball}} = \frac{4}{3} \pi (1.75)^3 \] First, calculate \( (1.75)^3 \): \[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 \approx 5.359375 \] Now plug it into the volume formula: \[ V_{\text{softball}} \approx \frac{4}{3} \times 3.14 \times 5.359375 \] \[ V_{\text{softball}} \approx \frac{4}{3} \times 16.83541875 \approx 22.447 \]
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Calculate the volume of the baseball: \[ V_{\text{baseball}} = \frac{4}{3} \pi (1.45)^3 \] First, calculate \( (1.45)^3 \): \[ (1.45)^3 = 1.45 \times 1.45 \times 1.45 \approx 3.073625 \] Now plug it into the volume formula: \[ V_{\text{baseball}} \approx \frac{4}{3} \times 3.14 \times 3.073625 \] \[ V_{\text{baseball}} \approx \frac{4}{3} \times 9.6532745 \approx 12.871 \]
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Calculate the difference in volumes: \[ \text{Difference} = V_{\text{softball}} - V_{\text{baseball}} \approx 22.447 - 12.871 = 9.576 \]
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Round to the nearest tenth: \[ 9.576 \text{ rounded to the nearest tenth is } 9.6 \]
Thus, the approximate difference in their volumes is \( \boxed{9.6 , \text{in}^3} \).
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