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 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. Given that the diameter of the chocolate piece is 1 inch, the radius \( r \) is:

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

Now we can plug 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 back into the volume formula:

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

To provide the answer in decimal form, we can approximate \( \pi \) as 3.14:

\[
V \approx \frac{1}{6} \times 3.14 \approx 0.5233
\]

Rounding to the nearest tenth:

\[
V \approx 0.5
\]

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

\[
\frac{1}{6} \pi \text{ inches}^3 \quad \text{or approximately} \quad 0.5 \text{ inches}^3.
\]