To find out how much space is empty in the container, we first need to calculate the volume of one tennis ball and then the total volume of 12 tennis balls.
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Volume of One Tennis Ball: The formula for the volume \( V \) of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
Where \( r \) is the radius. Given that the radius of each tennis ball is 2.5 inches:
\[ V = \frac{4}{3} \times 3.14 \times (2.5)^3 \]
First, calculate \( (2.5)^3 \):
\[ (2.5)^3 = 15.625 \]
Now plug this value back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 15.625 \]
Calculate \( \frac{4}{3} \times 3.14 \):
\[ \frac{4}{3} \times 3.14 \approx 4.18867 \]
Now multiply by 15.625:
\[ V \approx 4.18867 \times 15.625 \approx 65.4415 \text{ in}^3 \]
The approximate volume of one tennis ball is 65.44 in³.
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Total Volume of 12 Tennis Balls: Multiply the volume of one ball by 12:
\[ V_{\text{total}} = 65.44 \times 12 \approx 785.28 \text{ in}^3 \]
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Empty Space in the Container: Now we subtract the total volume of the tennis balls from the volume of the container:
\[ V_{\text{empty}} = 3200 - 785.28 \approx 2414.72 \text{ in}^3 \]
Rounding to the nearest whole number:
\[ V_{\text{empty}} \approx 2415 \text{ in}^3 \]
Thus, the amount of empty space in the container is approximately 2415 in³.
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