To find the approximate difference in volumes between a men's basketball and a women's basketball, we first need to calculate their volumes using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Step 1: Calculate the volumes
Men's basketball:
- Diameter = 10 inches, so the radius \( r = \frac{10}{2} = 5 \) inches.
- Volume \( V_m = \frac{4}{3} \times 3.14 \times (5^3) \)
Calculating this:
\[ V_m = \frac{4}{3} \times 3.14 \times 125 \] \[ V_m = \frac{4}{3} \times 392.5 \] \[ V_m \approx \frac{1570}{3} \] \[ V_m \approx 523.33 \text{ cubic inches} \]
Women's basketball:
- Diameter = 9 inches, so the radius \( r = \frac{9}{2} = 4.5 \) inches.
- Volume \( V_w = \frac{4}{3} \times 3.14 \times (4.5^3) \)
Calculating this:
\[ V_w = \frac{4}{3} \times 3.14 \times 91.125 \] \[ V_w \approx \frac{4}{3} \times 286.21 \] \[ V_w \approx \frac{1144.84}{3} \] \[ V_w \approx 381.61 \text{ cubic inches} \]
Step 2: Calculate the difference in volumes
Now, we subtract the volume of the women's basketball from the volume of the men's basketball:
\[ \text{Difference} = V_m - V_w \] \[ \text{Difference} \approx 523.33 - 381.61 \] \[ \text{Difference} \approx 141.72 \text{ cubic inches} \]
However, we can approximate the difference to fit among the provided responses.
Conclusion:
Among the provided options, it seems there's no exact match for the calculated difference. Let's check if there’s an understanding error or if approximations provided lead to different values. The closest volume approximations lead to differences that aren't fitting neatly within the range, suggesting the problem's setup may suggest rounding errors or misalignments with the values provided.
However, if the question specifically seeks larger-known approximations, we see:
Response Evaluation:
- 381.51 in³ (Difficult to correlate with above)
- 381.51 in³ (Repeats)
- 523.33 in³ (This seems a projection but not significant)
- 904.84 in³ (None fits)
- 3141.82 in³ ('Not relevant')
Based on calculated values:
- ⟹ 523.33 for men's basketball, 381.61 for women's gives a significant volume differential parameter towards women's needing and smaller dimensions.
Given bounding discrepancies and checking revisits to choices, If emphasized among traditional test responses, the estimate is further refined to:
- Final Approximate Difference = 141.72 in³ (not part of options given).
- Hence scrutinizing external choice and verifying on connected databases or re-checking dimensions could confirm on varying series derivations.
This matches key 4 vs 3 rationale perspectives; select the closest: (if practical examples on responses affirm). Based on significant dense measures, re-check for hypothesis leading remarks if revisited from material confirmation could harmonize towards rounded answer patterns within educational choices.