Question

You buy a sphere-shaped piece of chocolate that has a creamy center. The chocolate piece measures 1 inch in diameter. How much creamy filling can fit inside the chocolate piece? Calculate your answer in terms of π
𝜋
and round to the nearest tenth.

Answer 1

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:

\[
\frac{\pi}{6} \text{ cubic inches} \quad \text{or rounded to the nearest tenth: } 0.5 \text{ cubic inches}
\]