To calculate the volume of the men's and women's basketballs, we first need to find their respective radii from their diameters.
Step 1: Find the Radii
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Men's basketball:
- Diameter = 10 inches, so the radius \( r_m = \frac{10}{2} = 5 \) inches.
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Women's basketball:
- Diameter = 9 inches, so the radius \( r_w = \frac{9}{2} = 4.5 \) inches.
Step 2: Use the Volume Formula
The formula for the volume of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \]
Using \( \pi \approx 3.14 \):
Volume of the Men's Basketball:
\[ V_m = \frac{4}{3} \times 3.14 \times (5)^3 \] \[ V_m = \frac{4}{3} \times 3.14 \times 125 \] \[ V_m = \frac{4 \times 3.14 \times 125}{3} \] \[ V_m = \frac{1570}{3} \approx 523.33 , \text{in}^3 \]
Volume of the Women's Basketball:
\[ V_w = \frac{4}{3} \times 3.14 \times (4.5)^3 \] \[ V_w = \frac{4}{3} \times 3.14 \times 91.125 \] \[ V_w = \frac{4 \times 3.14 \times 91.125}{3} \] \[ V_w = \frac{1146.135}{3} \approx 382.05 , \text{in}^3 \]
Step 3: Calculate the Difference in Volumes
Now, we find the difference in volumes: \[ \text{Difference} = V_m - V_w \approx 523.33 - 382.05 \] \[ \text{Difference} \approx 141.28 , \text{in}^3 \]
None of the provided responses match this number, so the closest response based on the options provided would be:
141.82 in³
Therefore, the approximate difference of their volumes is 141.82 in³.