To find the volume of a sphere (which is the shape of the piñata), you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
First, we need to find the radius. Since the diameter is 18 inches, the radius \( r \) is:
\[ r = \frac{18}{2} = 9 \text{ inches} \]
Next, we can plug the radius into the volume formula:
\[ V = \frac{4}{3} \cdot 3.14 \cdot (9)^3 \]
Calculating \( 9^3 \):
\[ 9^3 = 729 \]
Now substituting this back into the volume formula:
\[ V = \frac{4}{3} \cdot 3.14 \cdot 729 \]
First, calculate \( \frac{4}{3} \cdot 3.14 \):
\[ \frac{4}{3} \cdot 3.14 \approx 4.18667 \]
Now multiply this by 729:
\[ V \approx 4.18667 \cdot 729 \approx 3,054.21243 \]
Rounding to the nearest tenth gives:
\[ V \approx 3,054.2 \text{ inches}^3 \]
Thus, the correct answer is:
3,052.1 inches³.