To find the volume of both men's and women's basketballs and their approximate difference, we will use the volume formula for a sphere, which is given as:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius for both basketballs:
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Men's basketball:
- Diameter = 10 inches, so the radius \( r = \frac{10}{2} = 5 \) inches.
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Women's basketball:
- Diameter = 9 inches, so the radius \( r = \frac{9}{2} = 4.5 \) inches.
Now we can calculate the volumes.
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Volume of the men's basketball: \[ V = \frac{4}{3} \times 3.14 \times (5)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 125 \] \[ V = \frac{4}{3} \times 392.5 \] \[ V \approx \frac{1570}{3} \approx 523.33 \text{ in}^3 \]
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Volume of the women's basketball: \[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \] \[ V = \frac{4}{3} \times 3.14 \times 91.125 \] \[ V \approx \frac{4}{3} \times 286.58375 \] \[ V \approx \frac{1146.335}{3} \approx 382.11 \text{ in}^3 \]
Now calculating the difference between the volumes:
\[ \text{Difference} \approx 523.33 \text{ in}^3 - 382.11 \text{ in}^3 \approx 141.22 \text{ in}^3 \]
Rounding to two decimal points, the approximate difference between the volumes of the men's and women's basketballs is:
141.82 in³
So the answer is:
141.82 in³