To find the difference in volumes between the youth softball and the adult softball, we start by using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to calculate the volumes of both softballs using their diameters:
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Youth Softball:
- Diameter = 3.5 in, so the radius \( r = \frac{3.5}{2} = 1.75 \) in.
- Volume \( V_y = \frac{4}{3} \pi (1.75)^3 \)
Calculating \( (1.75)^3 \): \[ (1.75)^3 = 1.75 \times 1.75 \times 1.75 = 5.359375 \]
Now substituting that into the volume formula: \[ V_y = \frac{4}{3} \times 3.14 \times 5.359375 \] Now calculate: \[ V_y \approx 4.18667 \times 5.359375 \approx 22.3971 \] \[ V_y \approx 4.18667 \times 5.359375 = 22.431 \text{ in}^3 \]
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Adult Softball:
- Diameter = 3.8 in, so the radius \( r = \frac{3.8}{2} = 1.9 \) in.
- Volume \( V_a = \frac{4}{3} \pi (1.9)^3 \)
Calculating \( (1.9)^3 \): \[ (1.9)^3 = 1.9 \times 1.9 \times 1.9 = 6.859 \]
Now substituting that into the volume formula: \[ V_a = \frac{4}{3} \times 3.14 \times 6.859 \] Now calculating: \[ V_a \approx 4.18667 \times 6.859 = 28.7624 \text{ in}^3 \]
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Difference in Volumes: \[ \text{Difference} = V_a - V_y \approx 28.7624 - 22.431 = 6.3314 \text{ in}^3 \]
Rounding to the nearest tenth: \[ \text{Difference} \approx 6.3 \text{ in}^3 \]
None of the response options you've provided match this exactly, indicating perhaps the volumes calculated may need to be verified or there might have been an error in response choices presented. Please cross-check the original parameters or the volume calculation.