Bot GPT 4-o mini To find the difference in the volumes of a softball and a baseball, we first need to calculate the volumes of both using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
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Calculate the volume of the softball:
- Diameter of the softball = 3.5 in
- Radius of the softball \( r_s = \frac{3.5}{2} = 1.75 \) in
\[ V_s = \frac{4}{3} \pi (1.75)^3 = \frac{4}{3} \pi (5.359375) \approx \frac{4}{3} \pi (5.359375) \approx 22.416 \text{ in}^3 \]
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Calculate the volume of the baseball:
- Diameter of the baseball = 2.9 in
- Radius of the baseball \( r_b = \frac{2.9}{2} = 1.45 \) in
\[ V_b = \frac{4}{3} \pi (1.45)^3 = \frac{4}{3} \pi (3.052625) \approx \frac{4}{3} \pi (3.052625) \approx 12.826 \text{ in}^3 \]
- Find the difference in volumes: \[ \Delta V = V_s - V_b \approx 22.416 \text{ in}^3 - 12.826 \text{ in}^3 \approx 9.590 \text{ in}^3 \]
To match this value with the given options, we need to determine which of the provided choices is approximately equal to this difference:
- Option B is \( 9.6^3 \).
Now we can calculate \( 9.6^3 \) to confirm:
\[ 9.6^3 = 9.6 \times 9.6 \times 9.6 \approx 10^3 = 96.1 \text{ in}^3 \]
However, this value does not make sense because it is significantly larger than the calculated difference.
Given the closeness and context provided in the problem, the closest approximate value for the difference in the options provided as we derived is indeed:
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