To calculate the difference in the volumes of a softball and a baseball, we will use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
First, we need to find the radius of each ball by dividing their diameters by 2.
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Softball:
- Diameter = 3.5 inches
- Radius \( r_{\text{softball}} = \frac{3.5}{2} = 1.75 \) inches
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Baseball:
- Diameter = 2.9 inches
- Radius \( r_{\text{baseball}} = \frac{2.9}{2} = 1.45 \) inches
Now we can calculate the volumes:
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Volume of the softball: \[ V_{\text{softball}} = \frac{4}{3} \cdot 3.14 \cdot (1.75)^3 \]
First, calculate \( (1.75)^3 \): \[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375 \]
Now, substitute back into the volume formula: \[ V_{\text{softball}} = \frac{4}{3} \cdot 3.14 \cdot 5.359375 \approx \frac{4 \cdot 3.14 \cdot 5.359375}{3} \approx \frac{67.41425}{3} \approx 22.47142 \text{ in}^3 \]
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Volume of the baseball: \[ V_{\text{baseball}} = \frac{4}{3} \cdot 3.14 \cdot (1.45)^3 \]
First, calculate \( (1.45)^3 \): \[ (1.45)^3 = 1.45 \times 1.45 \times 1.45 = 3.052625 \]
Now, substitute back into the volume formula: \[ V_{\text{baseball}} = \frac{4}{3} \cdot 3.14 \cdot 3.052625 \approx \frac{4 \cdot 3.14 \cdot 3.052625}{3} \approx \frac{38.20326}{3} \approx 12.73442 \text{ in}^3 \]
Finally, we find the difference in volume between the softball and the baseball:
\[ \text{Difference} = V_{\text{softball}} - V_{\text{baseball}} = 22.47142 - 12.73442 \approx 9.737 \]
Rounding this to the nearest tenth gives us:
\[ \text{Approximate difference in volumes} \approx 9.7 \text{ in}^3 \]
Thus, the approximate difference in their volumes is 9.7 in³.