To find the difference in volume between a men's basketball and a women's basketball, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius. First, we need to determine the radius for each basketball:
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Men's Basketball:
- Diameter = 10 inches
- Radius = \( \frac{10}{2} = 5 \) inches
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Women's Basketball:
- Diameter = 9 inches
- Radius = \( \frac{9}{2} = 4.5 \) inches
Next, we will calculate the volumes of both basketballs using \( \pi \approx 3.14 \).
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Volume of the Men's Basketball: \[ V_{\text{men}} = \frac{4}{3} \times 3.14 \times (5)^3 \] \[ = \frac{4}{3} \times 3.14 \times 125 \] \[ = \frac{4 \times 3.14 \times 125}{3} \] \[ = \frac{1570}{3} \approx 523.33 \text{ in}^3 \]
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Volume of the Women's Basketball: \[ V_{\text{women}} = \frac{4}{3} \times 3.14 \times (4.5)^3 \] \[ = \frac{4}{3} \times 3.14 \times 91.125 \] \[ = \frac{4 \times 3.14 \times 91.125}{3} \] \[ = \frac{1130.208}{3} \approx 376.736 \text{ in}^3 \]
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Difference in Volume: \[ \text{Difference} = V_{\text{men}} - V_{\text{women}} \] \[ \approx 523.33 - 376.736 \approx 146.594 \text{ in}^3 \]
From the calculations, the estimated approximate difference in volumes is about \( 146.59 \text{ in}^3 \), which does not match exactly with the provided options.
However, the closest option to our calculated difference would be 141.82 in³.
Thus, the correct response based on the given options would be: 141.82 in³.