Bot GPT 4-o mini To find the difference in volumes of a men's and a women's basketball, we start with the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to calculate the radius of both the men's and women's basketballs.
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Men's Basketball:
- Diameter = 10 inches, so the radius \( r = \frac{10}{2} = 5 \) inches.
- Volume: \[ V_m = \frac{4}{3} \pi (5)^3 = \frac{4}{3} \pi (125) = \frac{500}{3} \pi \] Substituting \( \pi \approx 3.14 \): \[ V_m \approx \frac{500}{3} \times 3.14 \approx 523.33 \text{ in}^3 \]
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Women's Basketball:
- Diameter = 9 inches, so the radius \( r = \frac{9}{2} = 4.5 \) inches.
- Volume: \[ V_w = \frac{4}{3} \pi (4.5)^3 = \frac{4}{3} \pi (91.125) \approx \frac{364.5}{3} \pi \] Substituting \( \pi \approx 3.14 \): \[ V_w \approx \frac{364.5}{3} \times 3.14 \approx 381.51 \text{ in}^3 \]
Now, we calculate the difference in volumes:
\[ \text{Difference} = V_m - V_w \] \[ \text{Difference} \approx 523.33 \text{ in}^3 - 381.51 \text{ in}^3 \approx 141.82 \text{ in}^3 \]
Thus, the approximate difference of their volumes is:
141.82 in³.
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