To find the volume of the piñata, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius of the piñata. The diameter is 18 inches, so the radius is:
\[ r = \frac{diameter}{2} = \frac{18}{2} = 9 \text{ inches} \]
Next, we substitute the radius and the value of \(\pi\) into the volume formula:
\[ V = \frac{4}{3} \cdot 3.14 \cdot (9)^3 \]
Calculating \(9^3\):
\[ 9^3 = 729 \]
Now plug that into the volume formula:
\[ V = \frac{4}{3} \cdot 3.14 \cdot 729 \]
Calculating \(\frac{4}{3} \cdot 3.14\):
\[ \frac{4}{3} \cdot 3.14 \approx 4.1867 \]
Now multiply that by 729:
\[ V \approx 4.1867 \cdot 729 \approx 3053.383 \]
Rounding this to the nearest tenth gives us:
\[ V \approx 3053.4 \text{ inches}^3 \]
Since this value is closest to 3,052.1 inches³ from the options, it looks like the precise calculation is slightly off due to rounding, but some sources may round Pi differently or at different points in the calculation which can affect the outcome slightly.
However, the closest answer from the options provided is:
3,052.1 inches³.
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