To find the difference in volumes between a men's basketball and a women's basketball, we first need to calculate the volumes of both basketballs using the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Step 1: Calculate the volume of the men's basketball:
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The diameter of the men's basketball is 10 inches, so the radius \( r \) is half of the diameter:
\[ r = \frac{10}{2} = 5 \text{ inches} \]
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Now we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (5)^3 \]
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Calculate \( (5)^3 \):
\[ (5)^3 = 125 \]
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Now substitute it back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 125 \]
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Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]
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Now multiply by 125:
\[ V \approx 4.1867 \times 125 \approx 523.33 \text{ in}^3 \]
Step 2: Calculate the volume of the women's basketball:
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The diameter of the women's basketball is 9 inches, so the radius \( r \) is:
\[ r = \frac{9}{2} = 4.5 \text{ inches} \]
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Substitute the radius into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (4.5)^3 \]
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Calculate \( (4.5)^3 \):
\[ (4.5)^3 = 91.125 \]
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Now substitute it back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 91.125 \]
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Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.1867 \]
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Now multiply by 91.125:
\[ V \approx 4.1867 \times 91.125 \approx 381.51 \text{ in}^3 \]
Step 3: Find the difference in volumes:
Now we can find the difference between the volumes of the men's and women's basketballs:
\[ \text{Difference} = V_{\text{men}} - V_{\text{women}} \approx 523.33 - 381.51 \approx 141.82 \text{ in}^3 \]
Answer:
The approximate difference in their volumes is 141.82 in³.