To find the empty space in the container, we first need to calculate the total volume of the tennis balls and then subtract that volume from the volume of the container.
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Calculate the volume of one tennis ball:
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Given that the radius \( r \) of each tennis ball is 2.5 inches, we substitute into the formula:
\[ V = \frac{4}{3} \times 3.14 \times (2.5)^3 \]
Calculating \( (2.5)^3 \):
\[ (2.5)^3 = 15.625 \]
Now substituting this value into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 15.625 \]
\[ V = \frac{4 \times 3.14 \times 15.625}{3} \]
First, calculate \( 4 \times 3.14 \):
\[ 4 \times 3.14 = 12.56 \]
Now, calculate \( 12.56 \times 15.625 \):
\[ 12.56 \times 15.625 \approx 196.09375 \]
Finally, divide by 3:
\[ V \approx \frac{196.09375}{3} \approx 65.36458333 \text{ in}^3 \]
Thus, the volume of one tennis ball is approximately \( 65.36 \text{ in}^3 \).
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Calculate the volume of a dozen (12) tennis balls:
\[ \text{Volume of 12 tennis balls} = 12 \times 65.36 \approx 784.32 \text{ in}^3 \]
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Calculate the empty space in the container:
The volume of the container is \( 3,200 \text{ in}^3 \). Therefore, empty space in the container is:
\[ \text{Empty space} = \text{Volume of container} - \text{Volume of 12 tennis balls} \]
\[ \text{Empty space} = 3200 - 784.32 \approx 2415.68 \text{ in}^3 \]
Rounding to the nearest whole number:
\[ \text{Empty space} \approx 2416 \text{ in}^3 \]
Therefore, the amount of empty space in the container is approximately 2416 in³. If this is not satisfactory, please clarify or provide additional context to your question.
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