To find the difference in volumes between a youth softball and an adult softball, we first need to calculate their respective volumes 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 radius of each softball:
- For the youth softball with a diameter of 3.5 in: \[ r_{\text{youth}} = \frac{3.5}{2} = 1.75 \text{ in} \]
- For the adult softball with a diameter of 3.8 in: \[ r_{\text{adult}} = \frac{3.8}{2} = 1.9 \text{ in} \]
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Calculate the volume of the youth softball: \[ V_{\text{youth}} = \frac{4}{3} \times 3.14 \times (1.75)^3 \] First, calculate \( (1.75)^3 \): \[ (1.75)^3 = 5.359375 \] Now we can calculate the volume: \[ V_{\text{youth}} = \frac{4}{3} \times 3.14 \times 5.359375 \approx \frac{4}{3} \times 16.83546 \approx 22.4472 \text{ in}^3 \]
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Calculate the volume of the adult softball: \[ V_{\text{adult}} = \frac{4}{3} \times 3.14 \times (1.9)^3 \] First, calculate \( (1.9)^3 \): \[ (1.9)^3 = 6.859 \] Now we can calculate the volume: \[ V_{\text{adult}} = \frac{4}{3} \times 3.14 \times 6.859 \approx \frac{4}{3} \times 21.56346 \approx 28.7486 \text{ in}^3 \]
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Calculate the difference in volumes: \[ \text{Difference} = V_{\text{adult}} - V_{\text{youth}} \approx 28.7486 - 22.4472 = 6.3014 \text{ in}^3 \]
Rounding this to the nearest tenth, we get:
\[ \text{Approximate difference} \approx 6.3 \text{ in}^3 \]
Thus, the answer is 6.3 in³.