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
and round to the nearest tenth.(1 point)
inches3

Answer 1

To calculate the volume of the creamy filling inside the chocolate sphere, we need to find the volume of a sphere. The formula for the volume \( V \) of a sphere with radius \( r \) is:

\[
V = \frac{4}{3} \pi r^3
\]

Given that the diameter of the chocolate sphere is 1 inch, we can find the radius:

\[
r = \frac{\text{diameter}}{2} = \frac{1 \text{ inch}}{2} = 0.5 \text{ inches}
\]

Now, we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (0.5)^3
\]

Calculating \( (0.5)^3 \):

\[
(0.5)^3 = 0.125
\]

Now, substituting this value back into the volume formula:

\[
V = \frac{4}{3} \pi (0.125) = \frac{4 \times 0.125}{3} \pi = \frac{0.5}{3} \pi = \frac{1}{6} \pi
\]

So the volume of the chocolate sphere (and thus the volume of the creamy filling) is:

\[
V = \frac{1}{6} \pi \text{ inches}^3
\]

To get a numerical approximation, we calculate:

\[
\frac{1}{6} \approx 0.1667
\]
Thus,

\[
\frac{1}{6} \pi \approx 0.1667 \times 3.1416 \approx 0.5236
\]

Rounding to the nearest tenth gives us:

\[
\approx 0.5 \text{ inches}^3
\]

Therefore, the volume of the creamy filling that can fit inside the chocolate piece is:

\[
\boxed{0.5} \text{ inches}^3
\]