To find the amount of creamy filling that can fit inside the chocolate piece, we need to calculate the volume of the sphere. The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.
The diameter of the chocolate piece is given as 1 inch. Therefore, the radius \( r \) is half of the diameter:
\[ r = \frac{1}{2} \text{ inch} \]
Now we can substitute \( r \) into the volume formula:
\[ V = \frac{4}{3} \pi \left( \frac{1}{2} \right)^3 \]
Calculating \( \left( \frac{1}{2} \right)^3 \):
\[ \left( \frac{1}{2} \right)^3 = \frac{1}{8} \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \pi \times \frac{1}{8} \]
This simplifies to:
\[ V = \frac{4 \pi}{24} = \frac{\pi}{6} \]
This gives us the volume in terms of \( \pi \).
To round this to the nearest tenth, we first calculate the decimal value of \( \frac{\pi}{6} \):
\[ \frac{\pi}{6} \approx \frac{3.14159}{6} \approx 0.5236 \]
Rounding this to the nearest tenth gives us:
\[ 0.5 \]
Thus, the volume of the creamy filling that can fit inside the chocolate piece is:
\[ \frac{\pi}{6} \text{ cubic inches} \quad \text{or rounded to the nearest tenth: } 0.5 \text{ cubic inches} \]
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